Question

What is the derivative of `y = arcsin(y^5)`?

Answer 1

`(5y^4)/sqrt(1 - y^10)`

Explanation:

using the `color(blue) " chain rule "`

and `d/dx(sin^(-1) x) = 1/sqrt(1 - x^2)`

hence `d/dy(sin^(-1)(y^5)) = 1/sqrt(1 - (y^5)^2) .d/dy(y^5)`

`= (5y^4)/sqrt(1 - y^10)`