# How do you find the derivative of sin2x cos2x?

You must use the and to find the derivative of this function.

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The product rule states that the derivative of ##f(x)*g(x)## is ##f'(x)*g(x) + f(x)*g'(x)##

So in this case, ##f(x) =sin2x## and ##g(x)=cos2x##

The chain rule states that the derivative of ##f(g(x))## is ##f'(g(x))*g'(x)##.

Using the chain rule, ##f'(x) = 2cos2x## and ##g'(x) = -2sin2x##

Therefore, using both rules, the derivative of ##sin2xcos2x## is ##(2cos2x)(cos2x)+(sin2x)(-2sin2x)## or ##2cos^2(2x)-2sin^2(2x)##

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