# What is the derivative of y=5^sqrt(s)?

Aug 7, 2015

$\frac{\mathrm{dy}}{\mathrm{ds}} = \frac{\log \left(5\right) {5}^{\sqrt{s}}}{2 \sqrt{s}}$

#### Explanation:

Use the chain use:

$f \left(x\right) = g \left(h \left(x\right)\right) \implies f ' \left(x\right) = h ' \left(x\right) g ' \left(h \left(x\right)\right)$

With:
$g \left(u\right) = {5}^{u} \implies g ' \left(u\right) = \log \left(5\right) {5}^{u}$
$h \left(x\right) = \sqrt{x} \implies \frac{1}{2 \sqrt{x}}$

Putting this together we have:
$\frac{\mathrm{dy}}{\mathrm{ds}} = \frac{\log \left(5\right) {5}^{\sqrt{s}}}{2 \sqrt{s}}$