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
\(\frac{dy}{dx}=\frac{d}{dx}(3x^2-9x+5)^9)\)
\(=9(3x^2-9x+5)^8.\frac{d}{dx}(3x^2-9x+5)\)
\(=9(3x^2-9x+5)^8.(6x-9)\)
\(=9(3x^2-9x+5)^8.3(2x-3)\)
\(=27(3x^2-9x+5)^8(2x-3)\)