Create an anonymous function after Symbolic differentiation
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Giorgos Papakonstantinou
on 13 May 2013
Commented: Walter Roberson
on 13 Apr 2018
I want to differentiate a function f and the calculate the derivative of f at value of x. How can I do that? for example:
syms x
f=@(x) x^3+3*x+1;
g=diff(f(x))
Preferably I would like to create a function handle of the derivative and then calculate the derivative at x.
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Accepted Answer
Sean de Wolski
on 13 May 2013
Almost there!
gfun = matlabFunction(g)
g(2)
4 Comments
Troy
on 13 Apr 2018
But what if the original function is just x? For example:
syms x
f=@(x) x;
g = matlabFunction(diff(f(x))
gives the result g = @()1.0 which is not a useable function. How to resolve?
Walter Roberson
on 13 Apr 2018
df = diff(f(x));
if isempty(symvar(df))
g = str2func(['@(x) repmat(', char(df), ', size(x))'])
else
g = matlabFunction(df);
end
Note: this will fail in some cases where the derivative just happens to be an expression involving a syntax that differs between MATLAB and the Symbolic Toolbox. For example,
f(x) = int(coth(cos(x)),x,1,5)*x
The int() part is actually a constant independent of the *x it is being muliplied by, so diff(f(x)) should be just int(coth(cos(x)),x,1,5), but if you emit that into the function handle you will fail when the handle is executed.
The situation could probably be improved by using
g = str2func(['@(x) repmat(', char(vpa(df)), ', size(x))'])
which will still lead to some failures, just perhaps fewer of them.
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