Question

How do you find the derivative of `f(x)=x^8/sin(5x)`?

Answer 1

The answer is:

`y'=(8x^7sin5x-x^8cos5x*5)/(sin^2 5x)=(x^7(8sin5x-5xcos5x))/(sin^2 5x)`.

This is for the rules:

`y=f(x)/g(x)rArry'=(f'(x)g(x)-f(x)g'(x))/[g(x)]^2`

and:

`y=sinf(x)rArry'=cosf(x)*f'(x).`