Question

How do you differentiate `f(x)=x/(x^2-1-sinx)` using the quotient rule?

Answer 1

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

Explanation:

By the quotient rule we get
`f'(x)=(x^2-1-sin(x)-x(2x-cos(x)))/(x^2-1-sin(x))^2`
which simplifies to
`f'(x)=(xcos(x)-x^2-1-sin(x))/(x^2-1-sin(x))^2`