Question

differentiate (xsinx+cosx)(sinx-xcosx)

Answer 1

use differentiation concept
y=f (x).g (x)
dy/dx=f (x).dg (x)/dx+g (x) df (x)/dx
now
dy/dx=(xsinx+cosx) d (sinx-xcosx)/dx+(sinx-xcosx) d (xsinx+cosx)/dx

=(xsinx+cosx)(cosx+xsinx-cosx)+(sinx-xcosx)(xcosx+sinx-sinx)

=(xsinx+cosx)(xsinx)+(cosx-xcosx)(xcosx)

=x^2sin^2x+xsinx.cosx+xcosx.sinx-x^2cos^2x

=x^2cos2x+2xsinx.cosx

=x^2cos2x+xsin2x