# How to differentiate x=2^t sint ?

Jun 9, 2018

$\frac{\mathrm{dy}}{\mathrm{dt}} = {2}^{t} \left(\cos t + \ln 2 \sin t\right)$

#### Explanation:

Let,
$y = {2}^{t} \sin t$

For differentiating this, we have to apply Product Rule .

$\frac{\mathrm{dy}}{\mathrm{dt}} = {2}^{t} \cos t + {2}^{t} \ln 2 \sin t$

$\frac{\mathrm{dy}}{\mathrm{dt}} = {2}^{t} \left(\cos t + \ln 2 \sin t\right)$