Differentiate given problems w.r.t.x.

$(3 x^{2} - 9 x + 5)^{9}$ .

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Solution

Let y = $(3 x^{2} - 9 x + 5)^{9}$

Differentiating w.r.t. x, we get

$\frac{d y}{d x} = 9 (3 x^{2} - 9 x + 5)^{8} \frac{d}{d x} = 9 (3 x^{2} - 9 x + 5)$

= $9 (3 x^{2} - 9 x + 5)^{8} (6 x - 9) = 9 \times 3 (2 x - 3) (3 x^{2} - 9 x + 5)^{8}$

= $27 (2 x - 3) (3 x^{2} - 9 x + 5)^{8}$

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