Differentiate the following functions with respect to x :

$\frac{3^{x}}{x + t a n x}$

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Solution

We have,

$\frac{d}{d x} (\frac{3^{x}}{x + t a n x})$

Applying quotient rule,

$\frac{(x + t a n x) \frac{d}{d x} (3^{x}) - 3^{x} \frac{d}{d x} (x + t a n x)}{(x + t a n x)^{2}}$

$= \frac{(x + t a n x) \times 3^{x} l o g 3 - 3^{x} (1 + s e c^{2} x)}{(x + t a n x)^{2}}$

$= \frac{3^{x} {(x + t a n x) l o g 3 - (1 + s e c^{2} x)}}{(x + t a n x)^{2}}$

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