Calculus and Its Applications, Chapter 1, 1.8, Section 1.8, Problem 44

Find $y''$: For $g(x) = 6x^5 + 2x^4 - 4x^3 + 7x^2 - 8x + 3$, find $g^{(7)} (x)$


$\begin{equation} \begin{aligned} g'(x) &= \frac{d}{dx} \left[ 6x^5 + 2x^4 - 4x^3 + 7x^2 - 8x + 3 \right] = 30x^4 + 8x^3 - 12x^2 + 14x - 8\\ \\ g''(x) &= \frac{d}{dx} \left[ 30x^4 + 8x^3 - 12x^2 + 14x - 8 \right] = 120x^3 + 24x^2 - 24x + 14\\ \\ g'''(x) &= \frac{d}{dx} \left[ 120x^3 + 24x^2 - 24x + 14 \right] = 360x^2 + 48x - 24\\ \\ g^{(4)}(x) &= \frac{d}{dx} \left[ 360x^2 + 48x - 24 \right] = 720x + 48\\ \\ g^{(5)}(x) &= \frac{d}{dx} \left[ 720x + 48 \right] = 720\\ \\ g^{(6)}(x) &= \frac{d}{dx} [720] = 0\\ \\ g^{(7)}(x) &= \frac{d}{dx} [0] = 0 \end{aligned} \end{equation}$