Math CentralQuandaries & Queries


Question from holly, a parent:

suppose f(x) = 2sin cubed x - 3 sin x

show that f '(x) = -3 cos x cos 2x

Hi Holly,

Using the chain rule you can show that the derivative of $f(x) = 2 \sin^3 x - 3 \sin x$ is

\[f'(x) = 6\; \sin^2 x \cos x - 3 \cos x\]

First pull out the common factor of $3 \cos x$ and then use the double angle expression for the cosine function to simplify the expression.


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