# How do you find the derivative of sin ^2 (2x) + sin (2x+1) ?

Mar 8, 2016

You can find it like this:

#### Explanation:

$f \left(x\right) = {\sin}^{2} \left(2 x\right) + \sin \left(2 x + 1\right)$

Applying the chain rule successively:

$f ' \left(x\right) = 2 {\left[\sin \left(2 x\right)\right]}^{1} \times \cos \left(2 x\right) \times 2 + \left[\cos \left(2 x + 1\right) \times 2\right]$

$\therefore f ' \left(x\right) = 4 \sin \left(2 x\right) \cos \left(2 x\right) + 2 \cos \left(2 x + 1\right)$