Find the derivative of this problem. h(x)=sin⁡2xcos⁡2x

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Find the derivative of this problem.  h(x)=sin⁡2xcos⁡2x

Thomas Conway · Accepted Answer

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)=sin⁡2xcos⁡2xDifferentiate the given dunction using the product rule as follows.h′(x)=ddx(sin⁡2xcos⁡2x)=sin⁡2xddx(cos⁡2x)+cos⁡2xddx(sin⁡2x)=sin⁡2x(−sin⁡2x)(2)+cos⁡(2x)(cos⁡2x)(2)=−2sin22x+2cos22x=−2(1−cos22x)+2cos22x=−2(1−cos22x)+2cos22x=−2+4cos22xTherefore, the derivative of the given function is h′(x)=−2+4cos22x

Find the derivative of this problem. h(x)=sin⁡2xcos⁡2x

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