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

Explanation

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


Differentiating with respect to `x`:


` f'(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 x-\sin ^{2} x-2 \sin x \cos x-\cos ^{2} x}{(\sin x-\cos x)^{2}}`



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