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How do you differentiate #sin^2(x) * cos^2(x)#?

1 Answer

May 21, 2016

#(d y)/(d x)=2 sin x cos^3 x-2 cos x*sin^3 x#

Explanation:

#y=sin^2 x*cos^2 x#

#(d y)/(d x)=(sin^2 x)^'*cos^2 x+(cos^2 x)^'*sin^2 x#

#(sin^2 x)^'=2sin x cos x#

#(cos^2 x)^'=-2sin x cos x#

#(d y)/(d x)=2 sin x cos x* cos^2 x-2 sin x cos x*sin^2 x#

#(d y)/(d x)=2 sin x cos^3 x-2 cos x*sin^3 x#

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