# How do you differentiate g(x) = xsqrt(x^2-x) using the product rule?

$g ' \left(x\right) = \sqrt{{x}^{2} - x} + \frac{2 {x}^{2} - x}{2 \sqrt{{x}^{2} - x}}$
By the product rule, $\left(u \left(x\right) v \left(x\right)\right) ' = u ' \left(x\right) v \left(x\right) + u \left(x\right) v ' \left(x\right)$.
Here, $u \left(x\right) = x$ so $u ' \left(x\right) = 1$ and $v \left(x\right) = \sqrt{{x}^{2} - x}$ so $v ' \left(x\right) = \frac{2 x - 1}{2 \sqrt{{x}^{2} - x}}$, hence the result.