Calculus Examples

$\frac{1}{3} π x^{2} y$

Step 1

Combine fractions.

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Step 1.1

Combine $\frac{1}{3}$ and $π$ .

$\frac{d}{d x} [\frac{π}{3} x^{2} y]$

Step 1.2

Combine $\frac{π}{3}$ and $x^{2}$ .

$\frac{d}{d x} [\frac{π x^{2}}{3} y]$

Step 1.3

Combine $\frac{π x^{2}}{3}$ and $y$ .

$\frac{d}{d x} [\frac{π x^{2} y}{3}]$

Step 2

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

$\frac{π y}{3} \frac{d}{d x} [x^{2}]$

Step 3

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

$\frac{π y}{3} (2 x)$

Step 4

Combine fractions.

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Step 4.1

Combine $2$ and $\frac{π y}{3}$ .

$\frac{2 (π y)}{3} x$

Step 4.2

Combine $\frac{2 (π y)}{3}$ and $x$ .

$\frac{2 (π y) x}{3}$

Step 4.3

Reorder terms.

$\frac{2 π x y}{3}$