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).

Answer 1

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