Question

How do you differentiate `f(x)=(x^2sinx)/(x^2cosx-sin^2x)` using the quotient rule?

Answer 1

Here is the quotient rule:
If `f(x) = g(x)/(h(x))` then `f'(x)=(g'(x)*h(x) - h'(x)*g(x))/((h(x))^2`.
Below is the way you would go about solving a question like this.

Explanation:

Here is the quotient rule:
If `f(x) = g(x)/(h(x))` then `f'(x)=(g'(x)*h(x) - h'(x)*g(x))/((h(x))^2`.

So in this case:
`g(x) = x^2sinx`
`h(x) = x^2cosx-sin^2x`

We differentiate both these parts with respect to `x` partially using the product rule.
`g'(x) = 2xsinx+x^2cosx`
`h'(x) = 2xcosx-x^2sinx-2sinxcosx`

So `f'(x)` becomes quite complex. Now all you need do is work out the brackets. I won't do this for you, I am quite busy. Sorry.