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 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.

Harley

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