Question

Differentiate w.r.t x (sinx) cosx

Answer 1

multiply and divide by 2
(2sinx cosx)/2=sin2x/2
differentiating we get, (2*cos2x)/2=cos2x

Answer 2

$\frac{d}{dx} sinxcosx \\ \\ = sinx \frac{d}{dx} cosx + cosx \frac{d}{dx} sinx \\ \\ = sinx( - sinx) + cosxcosx \\ \\ = - {sin}^{2} x + {cos}^{2} x \\ \\ = cos2x$