## Derivative in function handle

### vincenzo (view profile)

on 11 Sep 2017
Latest activity Commented on by James Tursa

### James Tursa (view profile)

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

### James Tursa (view profile)

on 11 Sep 2017
Edited by James Tursa

### James Tursa (view profile)

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

Walter Roberson

### Walter Roberson (view profile)

on 11 Sep 2017
No need for the eval()
syms x
f = @(x) x + log(x)
f1 = matlabFunction( diff(f(x)) );
f2 = matlabFunction( diff(f1(x)) );
James Tursa

on 12 Sep 2017
@Walter: +1

### José-Luis (view profile)

on 11 Sep 2017
Edited by José-Luis

### José-Luis (view profile)

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.