Question

Hello there can anyone solve this plz (chart is attached):

Answer 1

Answer:

$h^\prime(1)=14$

Step-by-step explanation:

We have the function:

$h(x)=f[f(x)]$

And we want to find:

$h^\prime(1)$

So, we will differentiate function h. By the chain rule, this yields:

$h^\prime(x)=f^\prime[f(x)]\cdot f^\prime(x)$

Then it follows that:

$h^\prime(1)=f^\prime[f(1)]\cdot f^\prime(1)$

Using the table, we acquire:

$h^\prime(1)=f^\prime(3)\cdot2$

And using the table again, we acquire:

$h^\prime(1)=7\cdot 2$

Evaluate. Hence:

$h^\prime(1)=14$