Question

Use the table below to evaluate

Answer 1

@rational

Answer 2

use chain rule

Answer 3

d/dx (f(g(u))) = du/dx g'(u) f'(g(u))
= (d(2x)/dx) g'(2x) f'(g(2x))

Answer 4

now what? @rational

Answer 5

\[\begin{align}
\left(f[g(2x)]\right)' &= f'[g(2x)]\left(g(2x)\right)'\\~\\
&=f'[g(2x)]g'(2x)\left(2x\right)'\\~\\
&=f'[g(2x)]g'(2x)(2)\\~\\
\end{align}\]

Answer 6

plugin x = 1

Answer 7

\[\begin{align}
\left(f[g(2x)]\right)' &= f'[g(2x)]\left(g(2x)\right)'\\~\\
&=f'[g(2x)]g'(2x)\left(2x\right)'\\~\\
&=f'[g(2x)]g'(2x)(2)\\~\\
&= f'[g(2)]g'(2)(2)\\~\\
&= ?
\end{align}\]

Answer 8

@rational