Question

If `f(x)= tan8 x` and `g(x) = 2 x`, how do you differentiate `f(g(x))` using the chain rule?

Answer 1

Derivative of `f(g(x))` is `32sec^2 16x`.

Explanation:

As `f(x)=tan8x`, `(df)/(dx)=sec^2 8x*8=16sec^2 8x`

and as `g(x)=2x` `(dg)/(dx)=2`

and `f(g(x))=tan8(2x)=tan16x`

and according to chain rule

`(df)/(dx)=(df)/(dg(x))*(dg)/(dx)`

= `16sec^2 8(g(x))*2`

= `16sec^2(8*2x)*2`

= `32sec^2 16x`