Answer:
[tex]h^\prime(1)=14[/tex]
Step-by-step explanation:
We have the function:
[tex]h(x)=f[f(x)][/tex]
And we want to find:
[tex]h^\prime(1)[/tex]
So, we will differentiate function h. By the chain rule, this yields:
[tex]h^\prime(x)=f^\prime[f(x)]\cdot f^\prime(x)[/tex]
Then it follows that:
[tex]h^\prime(1)=f^\prime[f(1)]\cdot f^\prime(1)[/tex]
Using the table, we acquire:
[tex]h^\prime(1)=f^\prime(3)\cdot2[/tex]
And using the table again, we acquire:
[tex]h^\prime(1)=7\cdot 2[/tex]
Evaluate. Hence:
[tex]h^\prime(1)=14[/tex]
