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Find the derivative of the following functions ( it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers ) $\large\frac{\sin x+\cos x}{\sin x - \cos x}$

1 Answer

Let $f(x) =\large\frac{\sin x+\cos x}{\sin x - \cos x}$
By quotient rule,
$ f'(x) = \large\frac{(\sin x-\cos x) \Large\frac{d}{dx}(\sin x+\cos x)-(\sin x+\cos x)\Large\frac{d}{dx}(\sin x - \cos x)}{( \sin x-\cos x)^2}$
$ = \large\frac{(\sin x - \cos x )( \cos x - \sin x )- (\sin x + \cos x )( \cos x + \sin x )}{( \sin x - \cos x )^2}$
$ = \large\frac{- ( \sin x - \cos x )^2- ( \sin x + \cos x )^2}{ \sin x-\cos x )^2}$
$ = \large\frac{-[ \sin^x+\cos^2x-2\sin x \cos x + \sin^2x+\cos^2x+2\sin x \cos x]}{(\sin x - \cos x )^2}$
$ = \large\frac{ -[1+1]}{(\sin x - \cos x)^2}$
$ = \large\frac{ -2}{(\sin x - \cos x)^2}$
answered Apr 14, 2014 by thanvigandhi_1
 

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