# How do you differentiate f(x) = (sinx)/(x^3-x) using the quotient rule?

If $f \left(x\right) = \sin \frac{x}{{x}^{3} - x}$
$f ' \left(x\right) = \frac{\frac{d}{\mathrm{dx}} \sin \left(x\right) \cdot \left({x}^{3} - x\right) - \frac{d}{\mathrm{dx}} \left({x}^{3} - x\right) \cdot \sin \left(x\right)}{{x}^{3} - x} ^ 2$
$= \frac{\cos \left(x\right) \cdot \left({x}^{3} - x\right) - \left(3 {x}^{2} - 1\right) \cdot \sin \left(x\right)}{{x}^{3} - x} ^ 2$