# Derivative in function handle

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vincenzo on 11 Sep 2017
Commented: James Tursa on 12 Sep 2017
f=@(x) x + log(x);
f1=diff(f)
f2=diff(f1)
I want to assign first derivative of 'f' to 'f1', and second derivative for 'f1' to 'f2' But i have this error "Undefined function 'diff' for input arguments of type 'function_handle'". How to fix? Thanks

José-Luis on 11 Sep 2017
Edited: José-Luis on 11 Sep 2017
If you're gonna do this numerically, you need to specify an interval in which to evaluate. Note that diff doesn't really give the derivative, but I'll stick to your nomenclature.
limits = [1,10];
f = @(interval) (interval(1):interval(2)) + log(interval(1):interval(2));
f1 = diff(f(limits));
f2 = diff(f1);
You could also do it symbolically but I can't help you there because I don't have the symbolic math toolbox.

James Tursa on 11 Sep 2017
Edited: James Tursa on 11 Sep 2017
E.g., if you want function handles you could get at them with the symbolic toolbox
>> syms x
>> f = @(x) x + log(x)
f =
@(x)x+log(x)
>> f1 = eval(['@(x)' char(diff(f(x)))])
f1 =
@(x)1/x+1
>> f2 = eval(['@(x)' char(diff(f1(x)))])
f2 =
@(x)-1/x^2
If you plan on feeding vectors or matrices etc to these function handles, then you could wrap the expressions appropriately with the vectorize( ) function. E.g.,
>> f1 = eval(['@(x)' vectorize(char(diff(f(x))))])
f1 =
@(x)1./x+1
>> f2 = eval(['@(x)' vectorize(char(diff(f1(x))))])
f2 =
@(x)-1./x.^2
##### 2 CommentsShowHide 1 older comment
James Tursa on 12 Sep 2017
@Walter: +1