Question

Please help me, I am writing everything down and following along diligently.

Answer 1

Solution:

Given:

$\begin{gathered} \frac{d}{dx}\lbrack g\lbrack f(2x)\rbrack\rbrack \\ at\text{ x = 1} \end{gathered}$

At x = 1,

$\begin{gathered} f(2x)=f(2(1))=f(2) \\ \\ \text{From the table given, } \\ f(2)=1 \end{gathered}$$\begin{gathered} g\lbrack f(2x)\rbrack=g(1) \\ \text{From the table,} \\ g(1)=1 \end{gathered}$$\begin{gathered} \frac{d}{dx}\lbrack g\lbrack f(2x)\rbrack\rbrack=\frac{d}{dx}g(1) \\ \frac{d}{dx}g(1)=g^1(1) \\ \\ \text{From the table, } \\ g^1(1)=4 \end{gathered}$

Therefore,

$\frac{d}{dx}\lbrack g\lbrack f(2x)\rbrack\rbrack\text{ at x = 1 is 4}$

Hence, the answer is 4.

Hence, the answer is 4.