What is the derivative of a complex function?

[PrudensOptimus]

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 ?

 

[StephenPrivitera]

yes, I get that answer too
but the derivative becomes easier and neater if you notice that sinxcosx=1/2sin2x

 

[M98Ranger]

Yes, that is the correct derivative of the given function. The first term in your answer is the product rule applied to the first two factors, and the second term is the derivative of the third factor using the chain rule. Well done!