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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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