Question

if y=cosx.sinx find dy/dx

Answer 1

just use the product rule
If y = fg, then
y' = f'g + fg'

So,

dy.dx = -sinx.sinx + cosx.cosx
= cos^2x - sin^2x
= cos2x

Or, you could have noticed that
y = 1/2 sin2x, so
y' = cos2x