Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants):
f(x)= $(p x + q) (\frac{r}{x} + s)$

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Solution

Here f(x)= $(p x + q) (\frac{r}{x} + s)$

$f^{'} (x) = \frac{d}{d x} [(p x + q) (\frac{r}{x} + s)]$

= $(p x + q) \frac{d}{d x} (\frac{r}{x} + s) + (\frac{r}{x} + s) \frac{d}{d x} (p x + q)$

$= (p x + q) (\frac{- r}{x^{2}}) + (\frac{r}{x} + s) (p)$

$= \frac{- p r}{x} \frac{- q r}{x^{2}} + \frac{p r}{x} + p s = \frac{- q r}{x^{2}} + p s$ .

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