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)
(