Question

How do you differentiate `f(x)=x^2/sin x`?

Answer 1

`f'(x)=(2xsinx-x^2cosx)/(sin^2x)`

Explanation:

differentiate f(x) using the `color(blue)"quotient rule"`

`"Given "f(x)=(g(x))/(h(x))" then"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(f'(x)=(h(x)g'(x)-g(x)h'(x))/(h(x))^2)color(white)(2/2)|)))`

`"here "g(x)=x^2rArrg'(x)=2x`

`"and "h(x)=sinxrArrh'(x)=cosx`

`rArrf'(x)=(2xsinx-x^2cosx)/(sin^2x)`