Items tagged with derivative

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 

Hello people in mapleprimes,

I want to ask you about how to make a function of function which makes a logarithmic derivative of a function.

For example, x^3 is mapped as h(x^3)=3h(x), h(x+y)=(x/(x+y))*h(x)+(y/(x+y))*h(y),

h(g(x)*k(x))=h(g(x))+h(k(x)).

I hope someone give me a hing to create h.

 

Best wishes.

taro

 

 

 

 

I wish to define a function which is the derivative of another function.

> f:=(x)->x^2:

> g:=(x)->diff(f(x),x):

> g(x);

2 x

> f(2);

4

> g(2);
Error, (in g) invalid input: diff received 2, which is not valid for its 2nd argument

 

I cannot find a way in which I can define the function g, using the functional operator, so that I can actually evaluate g(x).

 

How can I do this?

 

Hi,

     I now have a problem.

     I want to calculate first derivative of a function and make it a function with respect to a variable.

     For example,

     f:=x->x^2

     derivative:=x->diff(f,x)

 

     I expect derivative is a function, (i.e.  derivative(x)=2x) , So if I put 'derivative(2)',I should get 4 as results. However I get "Error, (in H_Mag_Derivative_2) invalid input: diff received 2, which is not valid for its 2nd argument".

     Could someone give me a hand? Very much appreciated.

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