Calculus Examples

$V = \frac{1}{3} π r^{2} h$

Step 1

Combine fractions.

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Step 1.1

Combine $\frac{1}{3}$ and $π$ .

$\frac{d}{d h} [\frac{π}{3} r^{2} h]$

Step 1.2

Combine $\frac{π}{3}$ and $r^{2}$ .

$\frac{d}{d h} [\frac{π r^{2}}{3} h]$

Step 1.3

Combine $\frac{π r^{2}}{3}$ and $h$ .

$\frac{d}{d h} [\frac{π r^{2} h}{3}]$

Step 2

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

$\frac{π r^{2}}{3} \frac{d}{d h} [h]$

Step 3

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

$\frac{π r^{2}}{3} \cdot 1$

Step 4

Multiply $\frac{π r^{2}}{3}$ by $1$ .

$\frac{π r^{2}}{3}$