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