# How do you find the derivative of xsqrt(2x - 3)?

Apr 1, 2016

$f ' \left(x\right) = \frac{3 \left(x - 1\right)}{\sqrt{2 x - 3}}$

#### Explanation:

Using product rule $f = u v \implies f ' = u ' v + u v '$, we have:

$f ' \left(x\right) = \left(x \sqrt{2 x - 3}\right) ' = 1 \cdot \sqrt{2 x - 3} + x \cdot \frac{1}{2 \sqrt{2 x - 3}} \cdot 2$

$f ' \left(x\right) = \sqrt{2 x - 3} + \frac{x}{\sqrt{2 x - 3}}$

$f ' \left(x\right) = \frac{3 x - 3}{\sqrt{2 x - 3}}$

$f ' \left(x\right) = \frac{3 \left(x - 1\right)}{\sqrt{2 x - 3}}$