Items tagged with derivative

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I'm still quite new to maple and I'm working calculating some dynamic equations.

I want to be able to selectively group certain variables or numbers depending on how I need the equations to be showed, I don't know if that's possible, I´ll explain further.

In typewritting extended format one equation is shown like this:

 

And maple standard:

The fisrt thing I want is to show the time derivatives in the dot representation, but I also want the 1/2 multiplyting each term of the whole equation like in the maoke standard format. 

I also need to group certain variables in some other equations I have and I was wondering if there is a way to do this.

doubt.mw

Equation21v2.mw

 

Hi,

When I do the derivation of a summation in order to one single term should not the result come out of the summation in the example attached in the file doubt? for example the derivative should not have yielded Ci and not the summation of Ci because for example if want the derivative in order to y1 it should be only C1 and not the summation of Ci.

 

The same happen when I go to a more complex case like in the file Equation21v2, should the result in the last double summation before T drop the summation over i to NC?

 

Many thanks in advance for your help!


 

Dear friend,

please suggest a way for manipulation of derivative of a function symbolically. Assume

Typesetting[Suppress]([f(x)]);
Ex1 :=expand(diff(f(x+y)+x*f(x-y), x)^2)+expand(diff(f(x-y)-y*f(x+y), x)^2);

Result is as needed:

Ex1 := (D(f))(x+y)^2+2*(D(f))(x+y)*f(x-y)+2*(D(f))(x+y)*x*(D(f))(x-y)+f(x-y)^2+2*f(x-y)*x*(D(f))(x-y)+x^2*(D(f))(x-y)^2+(D(f))(x-y)^2-2*(D(f))(x-y)*y*(D(f))(x+y)+y^2*(D(f))(x+y)^2

But later I cannot use D(f) as a function. Expressions

subs((D(f)) = (t -> 1-t), Ex1);
subs(diff(f(x),x) = (t -> 1-t), Ex1);

do not handle it as a function.

Hello

Can Maple compute the weak derivative of piecewise function like

f:=x->piecewise(0<x and x<0.5,x,0.5<x and x<1,1-x,  elsewhere 0);

Many thanks

 

When function is given as two variables, how to find extremas? help thanks

example: z=x3+y3-3xy

and alse the function as given condition z=x+2y, x2+y2=5

 

I have an equation were build with many unfixed numbers of variables as below:

eq:=f(U[i,j],V[i,j],W[i,j],S[i,j],T[i,j]), i,j=0,1,2,...(changing during the program running)

How do you suggest to calculate the first derivative of such equation with respect to U[i,j],V[i,j],W[i,j],S[i,j],T[i,j]?

Suppose that i,j=22, in this way to calculate the metioned derivative with respect to U[0,0] only, I must write:

diff( eq(U[0,0],U[0,1],U[0,2],...U[22,22], V[0,0],V[0,1],...,T[22,22]), U[0,0])  ( More than 2420 terms)

As you see it needs cumbersome writings if i,j be constants, and because the i and j are changing during the program, I dont know how to cope with this derivatives in Maple??

yVal := 0.01

xVal := 0.01

p8 := plot([fdiff(('rhs')((pds:-value(f(x, y)))(x, yVal)[3]), [y, y], x = z)], z = 0 .. 20, color = [red])

I cant seem to plot the graph for yVal, but if I were to switch it around to (xVal,y), the graph works perfectly. How should I input the code such that I can obtain the f''(x,0) graph. 

Any help will be greatly appreciated :) thanks

fyp3.mw

I have recently been working on a problem using fractional calculus and have come across something in Maple's fracdiff  command that makes no sense to me.

fracdiff(1, x, 1/2) = 0

It should be:     1/(sqrt(x)*sqrt(Pi))

Thanks.

fracdiff.mw

I'm inputting an optimization problem into Maple, and somewhere along the way my code stops working.  (Code is at the bottom.)

I need to find the second derviative for my Profit statement [(p-c)d]. I know the first derivative, deriving for p is, is d. d=ap-b, so deriving that statement for p should equal −abp−b−1 . For some reason, Maple is showing my second derivative as equal to zero.

Can anybody help me? TIA!

restart;

Profit := (p-c)*d;

d;=ap-b;

print(Solution); 

dProfit1 := diff(Profit, p); 

dProfit2 := diff(dProfit1, p); 

ddProfit2 := diff(Profit, p, p); 

pOpt := solve(diff(Profit, p));

                           Profit:=(p-c)ap-b

                          d:=ap-b

                            Solution

                          dProfit1:=ap-b

                             dProfit2:=0

                           ddProfit2:=0

                         pOpt:={ap=0, b=b)

 

 

For the PDE, I can't seem to plot T' as the y-axis, it gives me the error, "Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct". Anyone knows what seem to be the problem? I am open to all ideas and would appreciate any help:)

fyp3.mw

Hello people in mapleprimes,

I hope that you will give me an answer about the calculation surrounding D.
D((x+y)^2) can be calculated with maple, but D((x+y)^a), where a is a constant, cannot at least directly.
And, I have the code, which Mr. Carl Love kindly gave me at
http://www.mapleprimes.com/questions/218045-Logarithmic-Derivative
, which is

h:= F-> expand(evalindets(D(F)/F, specfunc(D), d-> op(d)*'h'(op(d))));

This works for (x+y)^2, but does not work for (x+y)^a.
And, I think this reason is that the behavior of D to (x+y)^2 is not the same
 as that to (x+y)^a.
And, I want to modify this code.
But, I can't .
So, I am asking this question. How should I modify the above code so that it works for (x+y)^a.
I'm so sorry for a lot of impoliteness.
I will be very glad if you give me an answer.

Take care.

taro

solve Derivative in maple

see in photo

 

For my fdiff graph, it seems that the cirtical points appear to be jaggered or not smooth. Anyone nows what seem to be the problem? i tried increasing the numpoints but it did not work:( I am open to all opinions. Thanks:)

 

fyp2.mw

I had problems plotting the solutions of my PDE with the derivative as the axis. Anyone knows what went wrong?

p1 := pds:-plot(diff(f(x,y),y), y = 0 .. 10, x = 0, numpoints = 100)

I seem to be getting a plot of y=0. Any help would be greatly appreciated:))

 

fyp2.mw

Hello,

To summarize, I have a variable ε = order(1),  which maple has assumed is a funtion ε(x,y,z) and so when I differentiate epsilon with respect to x (or y or z) I do not get 0. I get ε(or εy, εz). How do I ensure maple does not assume this?

More detail of my process:

I declare functions,

I have the function I want to transform,

Now I transform the variables to the new co-ordinate system. i.e. from (x,n,q) to (s,Y,z)

                   

Good! - Everything correct so far. 

Now I want to linearise so i introduce x=x0+ε*x1; and the same for (Y,z), 

               

As you can see, epsilon has derivatives, which it should not. 

How I can avoid this? 

Thanks in advance - im well and truely stumped over this.

P.s. if the images do not show, the script can be found here: 

https://www.dropbox.com/sh/34gepa60xf4droq/AAAJlUcQ_Jwkc96topPvcxtXa?dl=0 

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