# What is the derivative of sin(2x + 2)?

##### 1 Answer
Oct 9, 2015

$2 \cos \left(2 x + 2\right)$

#### Explanation:

To derive a composite function, first derive the outer function, leaving the inner one untouched, and then multiply for the derivative of the inner function. In formulas,

(f(g(x))' = f'(g(x)) * g'(x).

In this case, the derivative of $\sin \left(x\right)$ is $\cos \left(x\right)$, and the derivative of $2 x + 2$ is $2$. So, the whole derivative is

$\cos \left(2 x + 2\right) \cdot 2$