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

1 Answer
KillerBunny
Oct 9, 2015

#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#

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