Calculus and Its Applications, Chapter 1, 1.8, Section 1.8, Problem 2

If the function is $y = x^4 - 7$, determine $\displaystyle \frac{d^2y}{dx^2}$

$\begin{equation} \begin{aligned} \frac{dy}{dx} &= \frac{d}{dx} (x^4 - 7)\\ \\ &= \frac{d}{dx} (x^4) - \frac{d}{dx} (7) \\ \\ &= 4x^{4- 1}\\ \\ &= 4x^3 \end{aligned} \end{equation}$


Then,

$\begin{equation} \begin{aligned} \frac{d^2y}{dx^2} &= \frac{d}{dx} (4x^3) \\ \\ &= 4 \cdot x^{3-1}\\ \\ &= 12x^2 \end{aligned} \end{equation}$