# Is there a way to compute the n-th symbolic derivative of a function where n is also symbolic?

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Matt J on 17 Mar 2024
Edited: Paul on 17 Mar 2024
Is there a way to compute the n-th symbolic derivative of a function, where n is also a symbolic variable? The following does not seem to work.
syms f(x) x
syms n positive real integer
% Define the function for which you want to find the nth derivative
f(x) = exp(x);
T=diff(f,x,n)
T(x) =
0

Paul on 17 Mar 2024
Edited: Paul on 17 Mar 2024
Hi Matt,
I don't think so, at least not using diff
syms f(x) x
syms n positive real integer
% Define the function for which you want to find the nth derivative
f(x) = exp(x);
This line is telling diff to differentiate first wrt to x and then wrt to n, which is why the result is zero.
T=diff(f,x,n)
T(x) =
0
Though I suppose one could ask what it means to differentiate wrt to an integer-valued independent variable.

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