MaplePrimes - Questions and Posts tagged with calculus
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en-us2016 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemThu, 08 Dec 2016 02:12:04 GMTThu, 08 Dec 2016 02:12:04 GMTThe most recent questions and posts on MaplePrimes tagged with calculushttp://www.mapleprimes.com/images/mapleprimeswhite.jpgMaplePrimes - Questions and Posts tagged with calculus
http://www.mapleprimes.com/tags/calculus
matrix differentiation
http://www.mapleprimes.com/questions/220311-Matrix-Differentiation?ref=Feed:MaplePrimes:Tagged With calculus
<p><strong>First Question:</strong> How to define nx1 matrix Y:=(y1,y2,...,yn) ? (n is a Natural number while it is ungiven)</p>
<p><strong>Second Question: </strong>How to derivative of matrix Y with respect to nx1 matrix X:=(x1,x2,...,xn) ?</p>
<p> </p>
<p><br>
<strong><span style="color:#B22222;">My efforts for the first question: </span> </strong>(I know to define 6x1 matrix etc. , but I dont know to define nx1 matrix</p>
<pre class="prettyprint">
restart: Matrix(1..6,1,symbol=y) </pre>
<p> </p>
<p><strong>My efforts for the second question: </strong></p>
<pre class="prettyprint">
restart; with(VectorCalculus);
Matrix([x^2, x*y, x*z]);
Jacobian([x^2, x*y, x*z], [x, y, z]);</pre>
<p><br>
Can you help me? </p>
<p><strong>First Question:</strong> How to define nx1 matrix Y:=(y1,y2,...,yn) ? (n is a Natural number while it is ungiven)</p>
<p><strong>Second Question: </strong>How to derivative of matrix Y with respect to nx1 matrix X:=(x1,x2,...,xn) ?</p>
<p> </p>
<p><br>
<strong><span style="color:#B22222;">My efforts for the first question: </span> </strong>(I know to define 6x1 matrix etc. , but I dont know to define nx1 matrix</p>
<pre class="prettyprint">
restart: Matrix(1..6,1,symbol=y) </pre>
<p> </p>
<p><strong>My efforts for the second question: </strong></p>
<pre class="prettyprint">
restart; with(VectorCalculus);
Matrix([x^2, x*y, x*z]);
Jacobian([x^2, x*y, x*z], [x, y, z]);</pre>
<p><br>
Can you help me? </p>
220311Sun, 04 Dec 2016 12:47:50 Zstudent_mdstudent_mdhow do i find length?
http://www.mapleprimes.com/questions/219961-How-Do-I-Find-Length?ref=Feed:MaplePrimes:Tagged With calculus
<p>how i</p>
<p align="left"><font>Find the length of the curve in interval of x </font></p>
<p>how i</p>
<p align="left"><font>Find the length of the curve in interval of x </font></p>
219961Sat, 12 Nov 2016 19:06:57 ZbshayernbshayernHow do I derive a recurrence relations
http://www.mapleprimes.com/questions/219567-How-Do-I-Derive-A-Recurrence-Relations?ref=Feed:MaplePrimes:Tagged With calculus
<p><br>
equation 1 : x<sub>i+1</sub>=x<sub>i</sub>− (f·g<sub>y</sub>−f<sub>y</sub>·g)/(f<sub>x</sub> ·g<sub>y</sub> −f<sub>y</sub> ·g<sub>x</sub>)<br>
equation 2: y<sub>i+1</sub>=y<sub>i</sub>− (fx·g−f·g<sub>x</sub>)/(f<sub>x</sub>·g<sub>y</sub>-f<sub>y</sub>·g<sub>x</sub>)</p>
<p>My quesiton are, deriving equations (1) and (2) above and constructing a single Maple function called newt2d that implements both of these recurrence relation.</p>
<p>I apolgize in advance if I don't write my question correctly. This is my first time posting a question. </p>
<p><br>
equation 1 : x<sub>i+1</sub>=x<sub>i</sub>− (f·g<sub>y</sub>−f<sub>y</sub>·g)/(f<sub>x</sub> ·g<sub>y</sub> −f<sub>y</sub> ·g<sub>x</sub>)<br>
equation 2: y<sub>i+1</sub>=y<sub>i</sub>− (fx·g−f·g<sub>x</sub>)/(f<sub>x</sub>·g<sub>y</sub>-f<sub>y</sub>·g<sub>x</sub>)</p>
<p>My quesiton are, deriving equations (1) and (2) above and constructing a single Maple function called newt2d that implements both of these recurrence relation.</p>
<p>I apolgize in advance if I don't write my question correctly. This is my first time posting a question. </p>
219567Thu, 27 Oct 2016 20:06:34 Zisrael1697israel1697Puzzle or a simple exercise?
http://www.mapleprimes.com/posts/206713-Puzzle-Or-A-Simple-Exercise?ref=Feed:MaplePrimes:Tagged With calculus
<p><em>A string is wound symmetrically around a circular rod. The string goes exactly</em><br><em>4 times around the rod. The circumference of the rod is 4 cm and its length is 12 cm.</em><br><em>Find the length of the string.</em><br><em>Show all your work.</em><br><br>(It was presented at a meeting of the European Mathematical Society in 2001, <br>"Reference levels in mathematics in Europe at age16").<br><br>Can you solve it? You may want to try before seing the solution.<br>[I sometimes train olympiad students at my university, so I like such problems].<br><br></p>
<p><strong>restart;</strong><br><strong>eq:= 2/Pi*cos(t), 2/Pi*sin(t), 3/2/Pi*t; # The equations of the helix, t in 0 .. 8*Pi:</strong><br><strong> </strong><br><strong>p:=plots[spacecurve]([eq, t=0..8*Pi],scaling=constrained,color=red, thickness=5, axes=none):</strong><br><strong>plots:-display(plottools:-cylinder([0,0,0], 2/Pi, 12, style=surface, color=yellow),</strong><br><strong> p, scaling=constrained,axes=none);</strong><br> <img src="/view.aspx?sf=206713_post/puzzle.png" alt="" width="337" height="314"></p>
<p><strong>VectorCalculus:-ArcLength(<eq>, t=0..8*Pi);</strong></p>
<p> 20</p>
<p> </p>
<p>Let's look at the first loop around the rod. <br>If we develop the corresponding 1/4 of the cylinder, it results a rectangle whose sides are 4 and 12/4 = 3.<br>The diagonal is 5 (ask Pythagora why), so the length of the string is 4*5 = 20.<br><br></p>
<p> </p><p><em>A string is wound symmetrically around a circular rod. The string goes exactly</em><br><em>4 times around the rod. The circumference of the rod is 4 cm and its length is 12 cm.</em><br><em>Find the length of the string.</em><br><em>Show all your work.</em><br><br>(It was presented at a meeting of the European Mathematical Society in 2001, <br>"Reference levels in mathematics in Europe at age16").<br><br>Can you solve it? You may want to try before seing the solution.<br>[I sometimes train olympiad students at my university, so I like such problems].<br><br></p>
<h3>1. Maple solution</h3>
<p><strong>restart;</strong><br><strong>eq:= 2/Pi*cos(t), 2/Pi*sin(t), 3/2/Pi*t; # The equations of the helix, t in 0 .. 8*Pi:</strong><br><strong> </strong><br><strong>p:=plots[spacecurve]([eq, t=0..8*Pi],scaling=constrained,color=red, thickness=5, axes=none):</strong><br><strong>plots:-display(plottools:-cylinder([0,0,0], 2/Pi, 12, style=surface, color=yellow),</strong><br><strong> p, scaling=constrained,axes=none);</strong><br> <img src="/view.aspx?sf=206713_post/puzzle.png" alt="" width="337" height="314"></p>
<p><strong>VectorCalculus:-ArcLength(<eq>, t=0..8*Pi);</strong></p>
<p> 20</p>
<p> </p>
<h3>2. Elementary solution</h3>
<p>Let's look at the first loop around the rod. <br>If we develop the corresponding 1/4 of the cylinder, it results a rectangle whose sides are 4 and 12/4 = 3.<br>The diagonal is 5 (ask Pythagora why), so the length of the string is 4*5 = 20.<br><br></p>
<p> </p>206713Mon, 03 Oct 2016 16:05:15 ZvvvvShowing steps of a solution
http://www.mapleprimes.com/maplesoftblog/206346-Showing-Steps-Of-A-Solution?ref=Feed:MaplePrimes:Tagged With calculus
<p>Students using Maple often have different needs than non-students. Students need more than just a final answer; they are looking to gain an understanding of the mathematical concepts behind the problems they are asked to solve and to learn how to solve problems. They need an environment that allows them to explore the concepts and break problems down into smaller steps.</p>
<p>The <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student">Student</a> packages in Maple offer focused learning environments in which students can explore and reinforce fundamental concepts for courses in <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Precalculus">Precalculus</a>, <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/Hint">Calculus</a>, <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra">Linear Algebra</a>, <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Statistics">Statistics</a>, and more. For example, Maple includes step-by-step tutors that allow students to practice <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/IntTutor">integration</a>, <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/DiffTutor">differentiation</a>, <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/LimitTutor">the finding of limits</a>, and more. The Integration Tutor, shown below, lets a student evaluate an integral by selecting an applicable rule at each step. Maple will also offer hints or show the next step, if asked. The tutor doesn't only demonstrate how to obtain the result, but is designed for practicing and learning.</p>
<p style="text-align: center;"><img src="/view.aspx?sf=206346_post/IntMethods.PNG" alt="" width="480" height="436"></p>
<p>For this blog post, I’d like to focus in on an area of great interest to students: showing step-by-step solutions for a variety of problems in Maple.</p>
<p>Several commands in the Student packages can show solution steps as either output or inline in an interactive pop-up window. The first few examples return the solution steps as output.</p>
<p><strong>Precalculus problems:</strong></p>
<p>The <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Basics/ExpandSteps">Student:-Basics</a> sub-package provides a collection of commands to help students and teachers explore fundamental mathematical concepts that are core to many disciplines. It features two commands, both of which return step-by-step solutions as output.</p>
<p>The <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Basics/ExpandSteps">ExpandSteps</a> command accepts a product of polynomials and displays the steps required to expand the expression:</p>
<pre><strong>with(Student:-Basics):</strong></pre>
<pre><strong>ExpandSteps( (a^2-1)/(a/3+1/3) );</strong></pre>
<p style="text-align: center;"><img src="/view.aspx?sf=206346_post/ExpandSteps.PNG" alt="" width="479" height="291"></p>
<p>The <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Basics/LinearSolveSteps">LinearSolveSteps</a> command accepts an equation in one variable and displays the steps required to solve for that variable.</p>
<pre><strong>with(Student:-Basics):</strong></pre>
<pre><strong>LinearSolveSteps( (x+1)/y = 4*y^2 + 3*x, x );</strong></pre>
<p style="text-align: center;"><img src="/view.aspx?sf=206346_post/LinearSolveSteps.PNG" alt="" width="480" height="455"></p>
<p>This command also accepts some nonlinear equations that can be reduced down to linear equations.</p>
<p><strong>Calculus problems:</strong></p>
<p>The <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1">Student:-Calculus1</a> sub-package is designed to cover the basic material of a standard first course in single-variable calculus. Several commands in this package provide interactive tutors where you can step through computations and step-by-step solutions can be returned as standard worksheet output.</p>
<p>Tools like the <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/IntTutor">integration</a>, <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/DiffTutor">differentiation</a>, and <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/LimitTutor">limit</a> method tutors are interactive interfaces that allow for exploration. For example, similar to the integration-methods tutor above, the differentiation-methods tutor lets a student obtain a derivative by selecting the appropriate rule that applies at each step or by requesting a complete solution all at once. When done, pressing “Close” prints out to the Maple worksheet an annotated solution containing all of the steps.</p>
<p>For example, try entering the following into Maple:</p>
<pre><strong>with(Student:-Calculus1):</strong></pre>
<pre><strong>x*sin(x);</strong></pre>
<p>Next, right click on the Matrix and choose “<strong>Student Calculus1 -> Tutors -> Differentiation Methods…</strong>”</p>
<p style="text-align: center;"><img src="/view.aspx?sf=206346_post/DiffMethods.PNG" alt="" width="480" height="440"></p>
<p>The Student:-Calculus1 sub-package is not alone in offering this kind of step-by-step solution finding. Other commands in other Student packages are also capable of returning solutions.</p>
<p><strong>Linear Algebra Problems:</strong></p>
<p>The <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra">Student:-LinearAlgebra</a> sub-package is designed to cover the basic material of a standard first course in linear algebra. This sub-package features similar tutors to those found in the Calculus1 sub-package. Commands such as the <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra/GaussianEliminationTutor">Gaussian Elimination</a>, <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra/GaussJordanEliminationTutor">Gauss-Jordan Elimination</a>, <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra/InverseTutor">Matrix Inverse</a>, <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra/EigenvaluesTutor">Eigenvalues</a> or <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra/EigenvectorsTutor">Eigenvectors</a> tutors show step-by-step solutions for linear algebra problems in interactive pop-up tutor windows. Of these tutors, a personal favourite has to be the Gauss-Jordan Elimination tutor, which were I still a student, would have saved me a lot of time and effort searching for simple arithmetic errors while row-reducing matrices.</p>
<p>For example, try entering the following into Maple:</p>
<pre><strong>with(Student:-LinearAlgebra):</strong></pre>
<pre><strong>M:=<<77,9,31>|<-50,-80,43>|<25,94,12>|<20,-61,-48>>;</strong></pre>
<p>Next, right click on the Matrix and choose “<strong>Student Linear Algebra -> Tutors -> Gauss-Jordan Elimination Tutor</strong>”</p>
<p style="text-align: center;"><img src="/view.aspx?sf=206346_post/GJElimTutor.PNG" alt="" width="480" height="452"></p>
<p>This tutor makes it possible to step through row-reducing a matrix by using the controls on the right side of the pop-up window. If you are unsure where to go next, the “Next Step” button can be used to move forward one-step. Pressing “All Steps” returns all of the steps required to row reduce this matrix.</p>
<p>When this tutor is closed, it does not return results to the Maple worksheet, however it is still possible to use the Maple interface to step through performing elementary row operations and to capture the output in the Maple worksheet. By loading the Student:-LinearAlgebra package, you can simply use the right-click context menu to apply elementary row operations to a Matrix in order to step through the operations, capturing all of your steps along the way!</p>
<p><strong>An interactive application for showing steps for some problems:</strong></p>
<p>While working on this blog post, it struck me that we did not have any online interactive applications that could show solution steps, so using the commands that I’ve discussed above, I authored an application that can expand, solve linear problems, integrate, differentiate, or find limits. You can interact with this application <a href="http://maplecloud.maplesoft.com/application.jsp?appId=5651983367143424">here</a>, but note that this application is a work in progress, so feel free to email me (maplepm (at) Maplesoft.com) any strange bugs that you may encounter with it.</p>
<p>More detail on each of these commands can be found in Maple’s help pages.</p>
<p> </p><p>Students using Maple often have different needs than non-students. Students need more than just a final answer; they are looking to gain an understanding of the mathematical concepts behind the problems they are asked to solve and to learn how to solve problems. They need an environment that allows them to explore the concepts and break problems down into smaller steps.</p>
<p>The <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student">Student</a> packages in Maple offer focused learning environments in which students can explore and reinforce fundamental concepts for courses in <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Precalculus">Precalculus</a>, <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/Hint">Calculus</a>, <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra">Linear Algebra</a>, <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Statistics">Statistics</a>, and more. For example, Maple includes step-by-step tutors that allow students to practice <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/IntTutor">integration</a>, <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/DiffTutor">differentiation</a>, <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/LimitTutor">the finding of limits</a>, and more. The Integration Tutor, shown below, lets a student evaluate an integral by selecting an applicable rule at each step. Maple will also offer hints or show the next step, if asked. The tutor doesn't only demonstrate how to obtain the result, but is designed for practicing and learning.</p>
<p style="text-align: center;"><img src="/view.aspx?sf=206346_post/IntMethods.PNG" alt="" width="480" height="436"></p>
<p>For this blog post, I’d like to focus in on an area of great interest to students: showing step-by-step solutions for a variety of problems in Maple.</p>
<p>Several commands in the Student packages can show solution steps as either output or inline in an interactive pop-up window. The first few examples return the solution steps as output.</p>
<p><strong>Precalculus problems:</strong></p>
<p>The <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Basics/ExpandSteps">Student:-Basics</a> sub-package provides a collection of commands to help students and teachers explore fundamental mathematical concepts that are core to many disciplines. It features two commands, both of which return step-by-step solutions as output.</p>
<p>The <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Basics/ExpandSteps">ExpandSteps</a> command accepts a product of polynomials and displays the steps required to expand the expression:</p>
<pre><strong>with(Student:-Basics):</strong></pre>
<pre><strong>ExpandSteps( (a^2-1)/(a/3+1/3) );</strong></pre>
<p style="text-align: center;"><img src="/view.aspx?sf=206346_post/ExpandSteps.PNG" alt="" width="479" height="291"></p>
<p>The <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Basics/LinearSolveSteps">LinearSolveSteps</a> command accepts an equation in one variable and displays the steps required to solve for that variable.</p>
<pre><strong>with(Student:-Basics):</strong></pre>
<pre><strong>LinearSolveSteps( (x+1)/y = 4*y^2 + 3*x, x );</strong></pre>
<p style="text-align: center;"><img src="/view.aspx?sf=206346_post/LinearSolveSteps.PNG" alt="" width="480" height="455"></p>
<p>This command also accepts some nonlinear equations that can be reduced down to linear equations.</p>
<p><strong>Calculus problems:</strong></p>
<p>The <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1">Student:-Calculus1</a> sub-package is designed to cover the basic material of a standard first course in single-variable calculus. Several commands in this package provide interactive tutors where you can step through computations and step-by-step solutions can be returned as standard worksheet output.</p>
<p>Tools like the <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/IntTutor">integration</a>, <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/DiffTutor">differentiation</a>, and <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/LimitTutor">limit</a> method tutors are interactive interfaces that allow for exploration. For example, similar to the integration-methods tutor above, the differentiation-methods tutor lets a student obtain a derivative by selecting the appropriate rule that applies at each step or by requesting a complete solution all at once. When done, pressing “Close” prints out to the Maple worksheet an annotated solution containing all of the steps.</p>
<p>For example, try entering the following into Maple:</p>
<pre><strong>with(Student:-Calculus1):</strong></pre>
<pre><strong>x*sin(x);</strong></pre>
<p>Next, right click on the Matrix and choose “<strong>Student Calculus1 -> Tutors -> Differentiation Methods…</strong>”</p>
<p style="text-align: center;"><img src="/view.aspx?sf=206346_post/DiffMethods.PNG" alt="" width="480" height="440"></p>
<p>The Student:-Calculus1 sub-package is not alone in offering this kind of step-by-step solution finding. Other commands in other Student packages are also capable of returning solutions.</p>
<p><strong>Linear Algebra Problems:</strong></p>
<p>The <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra">Student:-LinearAlgebra</a> sub-package is designed to cover the basic material of a standard first course in linear algebra. This sub-package features similar tutors to those found in the Calculus1 sub-package. Commands such as the <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra/GaussianEliminationTutor">Gaussian Elimination</a>, <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra/GaussJordanEliminationTutor">Gauss-Jordan Elimination</a>, <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra/InverseTutor">Matrix Inverse</a>, <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra/EigenvaluesTutor">Eigenvalues</a> or <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra/EigenvectorsTutor">Eigenvectors</a> tutors show step-by-step solutions for linear algebra problems in interactive pop-up tutor windows. Of these tutors, a personal favourite has to be the Gauss-Jordan Elimination tutor, which were I still a student, would have saved me a lot of time and effort searching for simple arithmetic errors while row-reducing matrices.</p>
<p>For example, try entering the following into Maple:</p>
<pre><strong>with(Student:-LinearAlgebra):</strong></pre>
<pre><strong>M:=<<77,9,31>|<-50,-80,43>|<25,94,12>|<20,-61,-48>>;</strong></pre>
<p>Next, right click on the Matrix and choose “<strong>Student Linear Algebra -> Tutors -> Gauss-Jordan Elimination Tutor</strong>”</p>
<p style="text-align: center;"><img src="/view.aspx?sf=206346_post/GJElimTutor.PNG" alt="" width="480" height="452"></p>
<p>This tutor makes it possible to step through row-reducing a matrix by using the controls on the right side of the pop-up window. If you are unsure where to go next, the “Next Step” button can be used to move forward one-step. Pressing “All Steps” returns all of the steps required to row reduce this matrix.</p>
<p>When this tutor is closed, it does not return results to the Maple worksheet, however it is still possible to use the Maple interface to step through performing elementary row operations and to capture the output in the Maple worksheet. By loading the Student:-LinearAlgebra package, you can simply use the right-click context menu to apply elementary row operations to a Matrix in order to step through the operations, capturing all of your steps along the way!</p>
<p><strong>An interactive application for showing steps for some problems:</strong></p>
<p>While working on this blog post, it struck me that we did not have any online interactive applications that could show solution steps, so using the commands that I’ve discussed above, I authored an application that can expand, solve linear problems, integrate, differentiate, or find limits. You can interact with this application <a href="http://maplecloud.maplesoft.com/application.jsp?appId=5651983367143424">here</a>, but note that this application is a work in progress, so feel free to email me (maplepm (at) Maplesoft.com) any strange bugs that you may encounter with it.</p>
<p>More detail on each of these commands can be found in Maple’s help pages.</p>
<p> </p>206346Tue, 20 Sep 2016 18:42:06 ZDSkoogDSkoogHow to differentiate this?
http://www.mapleprimes.com/questions/208657-How-To-Differentiate-This?ref=Feed:MaplePrimes:Tagged With calculus
<p>diff(F(x,F(x)), x);</p>
<p> </p>
<p>how to differentiate this?</p>
<p> </p>
<p>(D[1](F))(x, F(x))+(D[2](F))(x, F(x))*(diff(F(x), x))</p>
<p> </p>
<p>how to find (D[1](F))(x, F(x)) and (D[2](F))(x, F(x)) ?</p>
<p> </p>
<p>i guess need define new calculus for two variables</p>
<p>Limit((F(x+h,F(x+h)) - F(x,F(x)))/h, h = 0);</p>
<p>Limit((F(x+h,F(x)) - F(x,F(x)))/h, h = 0);<br>Limit((F(x,F(x+h)) - F(x,F(x)))/h, h = 0);</p>
<p>Limit((F(x+h,F(x,y)) - F(x,F(x,y)))/h, h = 0);<br>Limit((F(x,F(x+h,y)) - F(x,F(x,y)))/h, h = 0);</p>
<p> </p>
<p>if inside F(x) is F(x,y)</p>
<p>it seems need to find the basic definition of F(x,y) first</p>
<p>if i define F(x,y) as</p>
<p>F := (x,y) -> min(x,y)/max(x,y);</p>
<p> </p>
<p>i may be wrong, how to differentiate correctly?</p><p>diff(F(x,F(x)), x);</p>
<p> </p>
<p>how to differentiate this?</p>
<p> </p>
<p>(D[1](F))(x, F(x))+(D[2](F))(x, F(x))*(diff(F(x), x))</p>
<p> </p>
<p>how to find (D[1](F))(x, F(x)) and (D[2](F))(x, F(x)) ?</p>
<p> </p>
<p>i guess need define new calculus for two variables</p>
<p>Limit((F(x+h,F(x+h)) - F(x,F(x)))/h, h = 0);</p>
<p>Limit((F(x+h,F(x)) - F(x,F(x)))/h, h = 0);<br>Limit((F(x,F(x+h)) - F(x,F(x)))/h, h = 0);</p>
<p>Limit((F(x+h,F(x,y)) - F(x,F(x,y)))/h, h = 0);<br>Limit((F(x,F(x+h,y)) - F(x,F(x,y)))/h, h = 0);</p>
<p> </p>
<p>if inside F(x) is F(x,y)</p>
<p>it seems need to find the basic definition of F(x,y) first</p>
<p>if i define F(x,y) as</p>
<p>F := (x,y) -> min(x,y)/max(x,y);</p>
<p> </p>
<p>i may be wrong, how to differentiate correctly?</p>208657Wed, 20 Jan 2016 16:16:09 Zasa12asa12