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

Question

1664 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-16T00:31:01

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

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.

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