Question

How do you differentiate `y= -cos^-1 (1/x^5)`?

Answer 1

`y'=-5/(x^6(sqrt(1-1/x^10))`

Explanation:

Use chain rule `f(g(x))'=f'(g(x))*g'(x)`and derivative property`cos^-1 x=-1/sqrt(1-x^2)`

`y'=-[-1/sqrt(1-(1/x^5)^2) *(-5)/x^6]`

`y'=-5/(x^6(sqrt(1-1/x^10))`