Calculus Examples

$\frac{d^{2}}{d r^{2}} \cdot (p r^{2})$

Step 1

Find the first derivative.

Tap for more steps...

Step 1.1

Since $r^{2}$ is constant with respect to $p$ , the derivative of $p r^{2}$ with respect to $p$ is $r^{2} \frac{d}{d p} [p]$ .

$r^{2} \frac{d}{d p} [p]$

Step 1.2

Differentiate using the Power Rule which states that $\frac{d}{d p} [p^{n}]$ is $n p^{n - 1}$ where $n = 1$ .

$r^{2} \cdot 1$

Step 1.3

Multiply $r^{2}$ by $1$ .

$f' (p) = r^{2}$

Step 2

Since $r^{2}$ is constant with respect to $p$ , the derivative of $r^{2}$ with respect to $p$ is $0$ .

$f'' (p) = 0$