Differentiate w.r.t. x the function in Exercise: (3x^2-9x+5)^9 - Vidyadip

Question

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

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Answer

Let $\text{y}=(3\text{x}^2-9\text{x}+5)^9$
Using chain rule, we obtain
$\frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}(3\text{x}^2-9\text{x}+5)^9$
$=9(3\text{x}^2-9\text{x}+5)^8.\frac{\text{d}}{\text{dx}}(3\text{x}^2-9\text{x}+5)$
$=9(3\text{x}^2-9\text{x}+5)^8.(6\text{x}-9)$
$=9(3\text{x}^2-9\text{x}+5)^8.3(2\text{x}-3)$
$=27(3\text{x}^2-9\text{x}+5)^8.3(2\text{x}-3)$

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