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# Finding the derivative of a function with respect to the derivative of a variable

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Aleem Andrew on 15 Jan 2021
Answered: Deepak Meena on 20 Jan 2021
I am trying to derive the expression that contains a dependent variable x with respect to the derivative of x, but although I defined dx as a variable I get the error message
Second argument must be a variable, a symfun or a list of variables and symfuns.
The output should be 2*diff(x,t,1).
syms x(t)
dx = diff(x,t,1);
L = dx^2
functionalDerivative(L,dx)
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### Answers (1)

Deepak Meena on 20 Jan 2021
Hi Andrew ,
Walter Robinson has beautifully explained why there is problem with using diff(f,diff()) here.
Now to get the desired Output you can do get something like this:
syms x(t) dx ad
dx = diff (x, t, 1);
L(ad) = subs(dx^2, dx, ad);
p = subs(diff(L, ad), ad, dx);
>>p
p(ad) =
2*diff(x(t), t)
Thanks
Deepak
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