Question

If `f(x)= tan8 x` and `g(x) = e^(-3x )`, how do you differentiate `f(g(x))` using the chain rule?

Answer 1

<`f'(g(x)) = -24 e^(-3x) . sec^2(8e^(-3x))`

Explanation:

`f(g(x)) = f( e^(-3x) )= tan(8e^(-3x))`

using 'chain rule' to differentiate.

`f'(g(x)) = sec^2(8e^(-3x)) d/dx (8e^(-3x))`

`= sec^2(8e^(-3x)) . 8e^(-3x) d/dx (-3x)`

`= sec^2(8e^(-3x)) .8e^(-3x) . (- 3 )`

`rArr f'(g(x)) = -24 e^(-3x). sec^2(8e^(-3x))`