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

Jan 4, 2016

Use the chain rule.

#### Explanation:

Say if the problem $y = \sin \left(a x + b\right)$
Then you can find the derivative of this using chain rule.

$\frac{\mathrm{dy}}{\mathrm{dx}} = \cos \left(a x + b\right) \cdot \frac{d}{\mathrm{dx}} \left(a x + b\right)$
$\frac{\mathrm{dy}}{\mathrm{dx}} = \cos \left(a x + b\right) \left(a\right)$
$\frac{\mathrm{dy}}{\mathrm{dx}} = a \cos \left(a x + b\right)$

Similarly

$y = \sin \left(2 x + 1\right)$
$\frac{\mathrm{dy}}{\mathrm{dx}} = \cos \left(2 x + 1\right) \frac{d}{\mathrm{dx}} \left(2 x + 1\right)$
$\frac{\mathrm{dy}}{\mathrm{dx}} = \cos \left(2 x + 1\right) \left(2\right)$

$\frac{\mathrm{dy}}{\mathrm{dx}} = 2 \cos \left(2 x + 1\right)$ Answer