# 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)?

Jun 5, 2018

$2 {f}^{'} \left(a\right)$

where $a$ is the common value of

$g \left(2\right) = g \left(4\right) = {f}^{'} \left(2\right) = {f}^{'} \left(4\right) = a$
It seems that the problem is incomplete.

#### Explanation:

By the chain rule of differentiation

${h}^{'} \left(x\right) = {f}^{'} \left(g \left(x\right)\right) \times {g}^{'} \left(x\right)$

Thus

${h}^{'} \left(2\right) = {f}^{'} \left(g \left(2\right)\right) \times {g}^{'} \left(2\right)$
$q \quad = 2 {f}^{'} \left(a\right)$

where $a$ is the common value of

$g \left(2\right) = g \left(4\right) = {f}^{'} \left(2\right) = {f}^{'} \left(4\right) = a$