Trigonometric derivative: power rule + product rule

[cinematic]

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!

 

[zachzach]

Homework Statement

Derive the following:

y = (cosxsin2x)^-22. 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!

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

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