Question

What is the derivative of `f(x)=1/(xsin^2x+xcos^2x)`?

Answer 1

`f'(x) = - 1 / x^2`

Explanation:

First of all, your function can be simplified: use the identity
`sin^2 x + cos^2 x = 1`.

`f(x) = 1/(x sin^2 x + x cos^2 x ) = 1 /(x(sin^2 x + cos^2 x )) = 1 / x = x^(-1)`

Now you can build the derivative:

`f'(x) = - x^(-2) = - 1 / x^2`