Find the derivative of the following function (it is to be understood that a, b, c, d are fixed non-zero constants):
f(x)= $(a x + b) (c x + d)^{2}$

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Solution

$(a x + b) (c x + d)^{2}$

Here f(x)= $(a x + b) (c x + d)^{2}$

$∴ f^{'} (x) = \frac{d}{d x} [(a x + b) (c x + d)^{2}]$

$= (a x + b) \frac{d}{d x} (c x + d)^{2} + (c x + d)^{2} . \frac{d}{d x} (a x + b)$

$= (a x + b) \times 2 (c x + d) \times c + (c x + d)^{2} \times a$

$= 2 c (a x + b) (c x + d) + a (c x + d)^{2}$

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