Differentiate the following function with respect of x: `sinxcosx`

Explanation

`frac{d}{d x}(sin x cos x)`


`cos x frac{d}{d x}(sin x)+sin x frac{d}{d x}(cos x)[` Using product rule]


`=cos x(cos x)+sin x(-sin x)`


`=cos ^{2} x-sin ^{2} x[because cos 2 x=cos ^{2} x-sin ^{2} x]`


`=cos 2 x`