Find the derivative of the following function-fx-sin x-cos x-sin x-cos x

Here f(x)= sin x+cos x/sin x cos x f'(x)= d/dx [ sin x+cos x/sin x cos x ] = (sin x cos x)d/dx(sin x+cos x) (sin x+cos x)d/dx(sin x cos x)/(sin x cos x)^2 = ...

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Standard XI

Mathematics

Range of Trigonometric Expressions

Find the deri...

Question

Find the derivative of the following function:
f(x) = $\frac{s i n x + c o s x}{s i n x - c o s x}$

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Solution

Here $f (x) = \frac{s i n x + c o s x}{s i n x - c o s x}$

$f^{'} (x) = \frac{d}{d x} [\frac{s i n x + c o s x}{s i n x - c o s x}]$

$= \frac{(s i n x - c o s x) \frac{d}{d x} (s i n x + c o s x) - (s i n x + c o s x) \frac{d}{d x} (s i n x - c o s x)}{(s i n x - c o s x)^{2}}$

$= \frac{(s i n x - c o s x) (c o s x - s i n x) - (s i n x + c o s x) (c o s x + s i n x)}{(s i n x - c o s x)^{2}}$

$= \frac{- (s i n x - c o s x)^{2} - (s i n x + c o s x)^{2}}{(s i n x - c o s x)^{2}}$

$= \frac{- 2 (s i n^{2} x + c o s^{2} x)}{(s i n x - c o s x)^{2}}$

$= \frac{- 2}{(s i n x - c o s x)^{2}}$

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