# How do you differentiate f(x)=e^(sinsqrtx) using the chain rule.?

Nov 30, 2016

$\frac{d}{\mathrm{dx}} {e}^{\sin \sqrt{x}} = \frac{\cos \sqrt{x}}{2 \sqrt{x}} {e}^{\sin \sqrt{x}}$
$\frac{\mathrm{df}}{\mathrm{dx}} = \frac{d \left({e}^{\sin \sqrt{x}}\right)}{d \left(\sin \sqrt{x}\right)} \cdot \frac{d \left(\sin \sqrt{x}\right)}{d \sqrt{x}} \cdot \frac{d \sqrt{x}}{\mathrm{dx}}$
$\frac{\mathrm{df}}{\mathrm{dx}} = {e}^{\sin \sqrt{x}} \cdot \cos \sqrt{x} \cdot \frac{1}{2} \frac{1}{\sqrt{x}}$
$\frac{\mathrm{df}}{\mathrm{dx}} = \frac{\cos \sqrt{x}}{2 \sqrt{x}} {e}^{\sin \sqrt{x}}$