SOLUTION: Differentitate y=cosxsinx I tried doing it by the product rule but it didn't work. thanks.

Question 27798: Differentitate

y=cosxsinx

I tried doing it by the product rule but it didn't work.
thanks.
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
Differentitate y=cosxsinx
y=cosxsinx
(dy/dx) = (cosx)[d/dx of (sinx)] + (sinx)[d/dx of (cosx)]
(using the product rule:
(first X derivative of the second)+ (second X derivative of the first)
=(cosx)X(cosx) + (sinx)X(-sinx)
= (cosx)^2 -(sinx)^2
= cos(2x) by formula
Another method:
y=cosxsinx = (1/2)(2sinxcosx) = (1/2)sin(2x)
(dy/dx) = (1/2)[d/dx of (sin2x)]
using (derivative of a constant times funciton
= constant times derivativeof the function)
= (1/2)(cos(2x))X[d/dx of (2x)] by chain rule
= (1/2)(cos(2x))X2
= cos(2x)
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