Differentiate the following functions with respect to x :

$\frac{x}{1 + t a n x}$

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Solution

Using quotient rule, we have,

$\frac{d}{d x} (\frac{x}{1 + t a n x})$

$= \frac{(1 + t a n x) \frac{d}{d x} (x) - x \frac{d}{d x} (1 + t a n x)}{(1 + t a n x)^{2}} = \frac{(1 + t a n x) - x (s e c^{2} x)}{(1 + t a n x)^{2}}$

$= \frac{1 + t a n x - x s e c^{2} x}{(1 + t a n x)^{2}}$

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