Question

`f(2)=f(4)=g'(2)=g'(4)=2` and `g(2)=g(4)=f'(2)=f'(4)`. If `h(x)=f(g(x))`, then `h'(2)`?

Answer 1

`2f^'(a)`

where `a` is the common value of

`g(2)=g(4)=f^'(2)=f^'(4)=a`
It seems that the problem is incomplete.

Explanation:

By the chain rule of differentiation

`h^'(x) = f^'(g(x))times g^'(x)`

Thus

`h^'(2) = f^'(g(2))times g^'(2)`
`qquad = 2f^'(a)`

where `a` is the common value of

`g(2)=g(4)=f^'(2)=f^'(4)=a`