Find the derivative of this problem. h(x)=\sin2x\cos2x

Susan Munoz

Susan Munoz

Answered question

2021-11-16

Find the derivative of this problem.
h(x)=sin2xcos2x

Answer & Explanation

Thomas Conway

Thomas Conway

Beginner2021-11-17Added 10 answers

Product Rule of differentiation:
If f(x) and g(x) are two differentiable functions, then (fg)(x)=f(x)g(x)+f(x)g(x)
The given function is h(x)=sin2xcos2x
Differentiate the given dunction using the product rule as follows.
h(x)=ddx(sin2xcos2x)
=sin2xddx(cos2x)+cos2xddx(sin2x)
=sin2x(sin2x)(2)+cos(2x)(cos2x)(2)
=2sin22x+2cos22x
=2(1cos22x)+2cos22x
=2(1cos22x)+2cos22x
=2+4cos22x
Therefore, the derivative of the given function is h(x)=2+4cos22x

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