How to do function composition in Sympy?

Question

I want to do something like h = f(g(x)) and be able to differentiate h, like h.diff(x). For just one function like h = cos(x) this is in fact possible and the documentation makes it clear.

But for function compositions it is not so clear. If you have done this, kindly show me an example or link me to the relevant document.

(If Sympy can't do this, do you know of any other packages that does this, even if it is non-python)

thank you.

Answer 1

It seems that function composition works as you would expect in sympy:

import sympy
h = sympy.cos('x')
g = sympy.sin(h)
g
Out[245]: sin(cos(x))

Or if you prefer

from sympy.abc import x,y
g = sympy.sin('y')
f = g.subs({'y':h})

Then you can just call diff to get your derivative.

g.diff()
Out[246]: -sin(x)*cos(cos(x))