Differentiate the following function with respect of x: `(sinx+cosx)/(sin x-cosx)`

Explanation

`f(x)=frac{sin x+cos x}{sin x-cos x}`



Differentiating with respect to `{x}` :


`f^{prime}(x)=frac{(sin x-cos x) frac{d}{d x}(sin x+cos x)-(sin x+cos x) frac{d}{d x}(sin x-cos x)}{(sin x-cos x)^{2}} `


`=frac{-(sin x-cos x)(cos x-sin x)-(sin x+cos x)(sin x+cos x)}{(sin x-cos x)^{2}} `


`=frac{-sin ^{2} x+2 sin x cos x-cos 2-sin ^{2} x-2 sin x cos x-cos ^{2} x}{(sin x-cos x)^{2}} `


`=frac{-2(sin ^{x}+cos ^{2} x)}{(sin x-cos ^{2} x)^{2}} `


`=frac{-2}{(sin x-cos x)^{2}}`