Differentiate the given function w.r.t. $x$ :
$(3 x^{2} - 9 x + 5)^{9}$

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Solution

Let $y = (3 x^{2} - 9 x + 5)^{9}$
Using chain rule, we obtain
$\frac{d y}{d x} = \frac{d}{d x} (3 x^{2} - 9 x + 5)^{9}$
$= 9 (3 x^{2} - 9 x + 5)^{8} . \frac{d}{d x} (3 x^{2} - 9 x + 5)$
$= 9 (3 x^{2} - 9 x + 5)^{8} . (6 x - 9)$
$= 9 (3 x^{2} - 9 x + 5)^{8} .3 (2 x - 3)$
$= 27 (3 x^{2} - 9 x + 5)^{8} (2 x - 3)$

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