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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 ) $\large\frac{\cos x}{1+\sin x}$

1 Answer

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

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