Common Calculus Mistakes
Chain Rule: Trigonometric Functions

The Goal



The Mistake

Find the mistake:


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The Correction


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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).)

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