# Math Help - Differentiation

1. ## Differentiation

Below are six facts about the values of two functions and and their derivatives.

Find the rate of change of at .

Could someone please explain how to solve this?

2. Originally Posted by Haris
Below are six facts about the values of two functions and and their derivatives.

Find the rate of change of at .

Could someone please explain how to solve this?
The rate of change is calculated by the first derivation of a function:

$(g(h(x))' = g'(h(x)) \cdot h'(x)$ Chain rule

You know x = 9
you know h(9) = 6
you know g'(6) = 6
you know h'(9) = 8

That means $g(h(9))' = 6 \cdot 8 = 48$