Question

If `f(x)= tan8 x` and `g(x) = e^(5x )`, how do you differentiate `f(g(x))` using the chain rule?

Answer 1

`f(g(x))=40e^(5x)sec^2(8e^(5x))`

Explanation:

As `f(x)=tan8x` and `g(x)=e^(5x)`

`f(g(x))=tan(8e^(5x))`

and `(df)/(dx)=(d(tan8e^(5x)))/(d(8e^(5x)))*(d(8e^(5x)))/(dx)`

= `sec^2(8e^(5x))*8*e^(5x)*5`

= `40e^(5x)sec^2(8e^(5x))`