# Trigonometric derivative: power rule + product rule

## Homework Statement

Derive the following:

y = (cosxsin2x)-2

2. The attempt at a solution

Basically I saw this as a power rule with two products in the middle.

So y = -2 (cos2cos2x-sinxsin2x)-1

But the correct answer is completely different, it's:

4(3sin2x - 1) all over
cos2xsin32x

Could someone please go through the steps to get to the correct solution? Thanks in advance!

## Homework Statement

Derive the following:

y = (cosxsin2x)-2

2. The attempt at a solution

Basically I saw this as a power rule with two products in the middle.

So y = -2 (cos2cos2x-sinxsin2x)-1

But the correct answer is completely different, it's:

4(3sin2x - 1) all over
cos2xsin32x

Could someone please go through the steps to get to the correct solution? Thanks in advance!

$$y = (cos{x}sin{2x})^{-2}$$

$$\frac{dy}{dx} = -2(\cos{x}\sin{2x})^{-3}[\underbrace{\frac{d}{dx}(\cos{x}\sin{2x})}_{use\: product \:rule}]$$

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