Question

How do you differentiate `f(x) = x^3/sinx` using the quotient rule?

Answer 1

`(x^2(3sinx-xcosx))/sin^2x`

Explanation:

The quotient rule states that:

`d/dx(u/v)=(vu'-uv')/v^2`

`u=x^3, v=sinx`
`u'=3x^2, v'=cosx`

`d/dx(x^3/sinx)=(sinx*3x^2-x^3*cosx)/sin^2x`

`=(x^2(3sinx-xcosx))/sin^2x`