# Anonymous Function Differentiation Problem?

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Steve on 29 Sep 2011
Edited: Walter Roberson on 8 Nov 2015
Hello Experts,
I have the following function:
>>f = @(x) x^2-1.
I want to find a function that will do differentiation: g = f' = 2*x so that g will be anonymous too and it will be possible to evaluate for example: g(5) = 10.
Steve

Richard Edmonds on 5 Nov 2015
Yes you can do it. Here is the code to acheive exactly what you want. (too late for you perhaps but this was the first link in my search so I came beack to drop in the best answer I found).
fdash=@(fun,x,epsilon)imag(fun(x(:)+1i*epsilon))/epsilon;
g=@(x)fdash(f,x,10^-20);

Matt Tearle on 29 Sep 2011
If you know the independent variable is called 'x':
fprime = str2func(['@(x) ',char(diff(sym(regexprep(char(f),'^@\(x\)',''))))])
fprime(pi)
If not... well, you can do it, but it will be a bit messier.

Doug Hull on 29 Sep 2011
If you know you will be dealing only with polynomials, can you make something like this work?

Walter Roberson on 29 Sep 2011
You cannot do that, not without converting the anonymous function in to a character string and doing symbolic differentiation on that, and constructing the appropriate anonymous function from the result.
If you attempt to do this numerically, then because you can only sample at a finite number of numeric points, there will be an infinite number of functions that match the numeric results, leaving you unable to select the correct function to differentiate. You will, for example, be unable to find removable discontinuities numerically (except by luck). And good luck doing a numeric reconstruction of tan(Pi*exp(x)) .