# How do you use the product rule to differentiate g(s)=sqrts(4-s^2)?

Feb 2, 2017

$g ' \left(s\right) = \frac{4 - 5 {s}^{2}}{2 \sqrt{s}}$

#### Explanation:

$g ' \left(s\right) = \frac{1}{2 \sqrt{s}} \cdot \left(4 - {s}^{2}\right) + \sqrt{s} \cdot \left(- 2 s\right)$

$= \frac{4 - {s}^{2}}{2 \sqrt{s}} - 2 s \sqrt{s}$

$\frac{4 - {s}^{2} - 2 s \sqrt{s} \cdot \left(2 \sqrt{s}\right)}{2 \sqrt{s}}$

$\frac{4 - {s}^{2} - 4 {s}^{2}}{2 \sqrt{s}}$

$\frac{4 - 5 {s}^{2}}{2 \sqrt{s}}$