Calculus Examples

$y = \frac{4}{7} π r^{3}$

Step 1

Find the first derivative.

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Step 1.1

Combine fractions.

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Step 1.1.1

Combine $π$ and $\frac{4}{7}$ .

$\frac{d}{d `} [\frac{π \cdot 4}{7} \cdot r^{3}]$

Step 1.1.2

Combine $\frac{π \cdot 4}{7}$ and $r^{3}$ .

$\frac{d}{d `} [\frac{π \cdot 4 r^{3}}{7}]$

Step 1.1.3

Move $4$ to the left of $π$ .

$\frac{d}{d `} [\frac{4 \cdot π r^{3}}{7}]$

Step 1.2

Since $\frac{4 π r^{3}}{7}$ is constant with respect to $`$ , the derivative of $\frac{4 π r^{3}}{7}$ with respect to $`$ is $0$ .

$f' (`) = 0$

Step 2

Since $0$ is constant with respect to $`$ , the derivative of $0$ with respect to $`$ is $0$ .

$f'' (`) = 0$