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}
$