The Goal

Find

The Mistake

Find the mistake:

(Roll the mouse over the math to see a hint in red)

The Correction

(Roll the mouse over the area above to see the correction in blue)

An Explanation

The chain rule was used incorrectly on cos(2x). The chain rule says:

For cos(2x) the outside function is f(x) = cos(x) and the inside function is g(x) = 2x. The inside function g(x) is composed with (plugged into) the derivative f'(x). The g'(x) = 2 part of the chain rule was performed correctly.

(There's another possible explanation for the mistake: the student may have incorrectly reasoned that cos(2x) is equal to 2cos(x), and then taken the derivative. Cosine is not a linear function, so cos(2x) ≠ 2cos(x).)