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Algebra of Derivatives

Differentiate...

Question

Differentiate $y = \frac{s i n x}{1 - c o s x}$ w.r.t $x$ .

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Solution

According to question,

$y = \frac{s i n x}{1 - c o s x} \times \frac{1 + c o s x}{1 + c o s x}$

$⟹ y = \frac{s i n x (1 + c o s x)}{1 - c o s^{2} x}$

$⟹ y = \frac{s i n x (1 + c o s x)}{s i n^{2} x}$

$⟹ y = \frac{(1 + c o s x)}{s i n x}$

$⟹ y = c o s e c x + c o t x$

$⟹ \frac{d y}{d x} = - c o s e c x . c o t x - c o s e c^{2} x$

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