# What is the solution to the function using Chain Rule?

## F(t)= e^(2tsin(2t)

Feb 26, 2018

$F ' \left(t\right) = \left(4 t \cos \left(2 t\right) + 2 \sin \left(2 t\right)\right) {e}^{2 t \sin \left(2 t\right)}$

#### Explanation:

$F ' \left(t\right) = \left({e}^{2 t \sin \left(2 t\right)}\right) \frac{d}{\mathrm{dt}}$
$v = 2 t \sin \left(2 t\right)$
$\left({e}^{v}\right) \frac{d}{\mathrm{dt}} = v ' \cdot {e}^{v}$
$v ' = a \frac{d}{\mathrm{dt}} b + b \frac{d}{\mathrm{dt}} a$
$a = 2 t$
$a ' = 2$
$b = \sin \left(2 t\right)$
$b ' = 2 \cos \left(2 t\right)$
$v ' = 4 t \cos \left(2 t\right) + 2 \sin \left(2 t\right)$
$F ' \left(t\right) = \left(4 t \cos \left(2 t\right) + 2 \sin \left(2 t\right)\right) {e}^{2 t \sin \left(2 t\right)}$