Question

differentiate the following by product rule. (a) x²cox (b) Sinx x cosx​

Answer 1

(sin^2x)= dx/d(sinx.sinx)

Applying product rule, we have

dx/d (sinx.sinx)

=sinx dx/d (sinx)+ dx/d (sinx)sinx

=sincosx+cosxsinx(∵ dx/d (sinx)=cosx)

=2sinxcosx

=sin2x(∵2sinxcosx=sin2x)

Therefore,

dx/d (sin^2x)=sin2x