Question

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

Answer 1

`2cos(2x+2)`

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(x)` is `cos(x)`, and the derivative of `2x+2` is `2`. So, the whole derivative is

`cos(2x+2) * 2`