Question

How do you find the derivative of `root5(x^-5)`?

Answer 1

`(d(root(5)(x^(-5))))/(dx)=-1/x^2`

Explanation:

`root(5)(x^(-5))=(x^(-5))^(1/5)=x^((-5)xx(1/5))=x^-1`

As `(d(x^-1))/(dx)=-1*x^(-2)=-1/x^2`

Hence `(d(root(5)(x^(-5))))/(dx)=-1/x^2`