Question

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

Answer 1

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