Derivative of a long function

What is the derivative of

y = (x^3/2)(sinxcosx)^2

is it

(x^3/2)(2sinxcosx)(cos^2x - sin^2x) + (3sqrt(x)/2)(sinxcosx)^2 ?
yes, I get that answer too
but the derivative becomes easier and neater if you notice that sinxcosx=1/2sin2x

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