Calculus Examples

$\frac{4}{3} \cdot (p r^{2})$

Step 1

Combine fractions.

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Step 1.1

Combine $p$ and $\frac{4}{3}$ .

$\frac{d}{d r} [\frac{p \cdot 4}{3} \cdot r^{2}]$

Step 1.2

Combine $\frac{p \cdot 4}{3}$ and $r^{2}$ .

$\frac{d}{d r} [\frac{p \cdot 4 r^{2}}{3}]$

Step 1.3

Move $4$ to the left of $p$ .

$\frac{d}{d r} [\frac{4 \cdot p r^{2}}{3}]$

Step 2

Since $\frac{4 p}{3}$ is constant with respect to $r$ , the derivative of $\frac{4 p r^{2}}{3}$ with respect to $r$ is $\frac{4 p}{3} \frac{d}{d r} [r^{2}]$ .

$\frac{4 p}{3} \frac{d}{d r} [r^{2}]$

Step 3

Differentiate using the Power Rule which states that $\frac{d}{d r} [r^{n}]$ is $n r^{n - 1}$ where $n = 2$ .

$\frac{4 p}{3} (2 r)$

Step 4

Combine fractions.

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Step 4.1

Combine $2$ and $\frac{4 p}{3}$ .

$\frac{2 (4 p)}{3} r$

Step 4.2

Multiply $4$ by $2$ .

$\frac{8 p}{3} r$

Step 4.3

Combine $\frac{8 p}{3}$ and $r$ .

$\frac{8 p r}{3}$