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

1 Answer
Jan 18, 2018

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.