Question

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

Answer 1

`g'(x) = sqrt(x^2 - x) + (2x^2 - x)/(2sqrt(x^2 - x))`

Explanation:

By the product rule, `(u(x)v(x))' = u'(x)v(x) + u(x)v'(x)`.

Here, `u(x) = x` so `u'(x) = 1` and `v(x) = sqrt(x^2 - x)` so `v'(x) = (2x-1)/(2sqrt(x^2 - x))`, hence the result.