Question

Need help with this please. Given the following functions: f(u)=tan(u) and g(x)=x^9. Find:

f′(g(x))=
(f∘g)′(x)=

I found the other functions, just need help with these two.

Answer 1

You have
.. f'(u) = sec(u)^2
Putting in u = g(x) = x^9, this becomes
.. f'(g(x)) = sec(x^9)^2


You know
(f(g(x))' = f'(g(x))*g'(x) . . . . . chain rule
From previous results, this is
.. sec(x^9)^2*9x^8