Question

If h(x) = f[g(x)], use the table of values for f, g, f ′ and g ′ to find the value of h ′(1).


x f(x) g(x) f ′(x) g ′(x)
1 3 2 2 6
2 1 8 5 7
3 7 2 7 9
Numerical Answers Expected!

Answer 1

Answer: Hey there :)

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

To find h ' ( x )  

We do → f ' [ g ( x ) ] × g ' ( x )  

This is called the chain rule

Given;

g ( 1 ) = 2  →  f ' ( 2 ) = 5

g ' ( 1 ) = 6

Apply the formula

h ' ( 1 ) = f ' [ g ( 1 ) ] × g ' ( 1 )

          = f ' ( 2 ) × 6

          = 5 × 6

h ' ( 1 ) = 30

Step-by-step explanation: