Create an anonymous function after Symbolic differentiation

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.

Answer 1

[Sean de Wolski]

Almost there!

gfun = matlabFunction(g)
g(2)

[Giorgos Papakonstantinou]

Thank you. Although it should be gfun(2).

[Sean de Wolski]

Rule #1 of Answers: if you rewrite something from MATLAB, you will make a typo :)

[Troy]

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]

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.

Answer 2

[Iman Ansari]

Hi.

syms x
f=@(x) x^3+3*x+1;
g=diff(f(x))
h=@(y) subs(g,y)

[Giorgos Papakonstantinou]

Thank you! But then if I ask for g(2) then I get this error:

Error using mupadmex
Error in MuPAD command: Index exceeds matrix dimensions.

Error in sym/subsref (line 1389)
        B = mupadmex('symobj::subsref',A.s,inds{:});

[Giorgos Papakonstantinou]

with h(2) it works... thank you!