Question

If `f(x) =cos3x` and `g(x) = (2x-1)^2`, what is `f'(g(x))`?

Answer 1

`(df)/(dg)=(-3sin3x)/(4(2x-1))`

Explanation:

As per chain formula `(df)/(dx)=(df)/(dg)xx(dg)/(dx)`. hence

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

As `f(x)=sin3x` and `g(x)=(2x-1)^2`

`(df)/(dx)=-sin3x xx3` and `(dg)/(dx)=2(2x-1)xx2`

Hence `(df)/(dg)=(-3sin3x)/(4(2x-1))`