Question

If `f(x)= cot5 x` and `g(x) = 2x^2 -1`, how do you differentiate `f(g(x))` using the chain rule?

Answer 1

`(df)/(dx)-4xcsc^2(10x^2-5)`

Explanation:

If `f(x)=cot5x` and `g(x)=2x^2-1`

`f(g(x))=cot(5*(2x^2-1))`

As according to chain rule, `(df)/(dx)=(df)/(dg)xx(dg)/(dx)`

`(df)/(dx)=-csc^2(5*(2x^2-1))xxd/(dx)(2x^2-1)`

= `-csc^2(10x^2-5)xx4x)`

= `-4xcsc^2(10x^2-5)`