Calculus Examples

\frac{x^{2}}{9}

$\frac{x^{2}}{9}$

Step 1

Since

\frac{1}{9}

$\frac{1}{9}$ is constant with respect to

x

$x$ , the derivative of

\frac{x^{2}}{9}

$\frac{x^{2}}{9}$ with respect to

x

$x$ is

\frac{1}{9} \frac{d}{d x} [x^{2}]

$\frac{1}{9} \frac{d}{d x} [x^{2}]$ .

\frac{1}{9} \frac{d}{d x} [x^{2}]

$\frac{1}{9} \frac{d}{d x} [x^{2}]$

Step 2

Differentiate using the Power Rule which states that

\frac{d}{d x} [x^{n}]

$\frac{d}{d x} [x^{n}]$ is

n x^{n - 1}

$n x^{n - 1}$ where

n = 2

$n = 2$ .

\frac{1}{9} (2 x)

$\frac{1}{9} (2 x)$

Step 3

Combine fractions.

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Step 3.1

Combine

2

$2$ and

\frac{1}{9}

$\frac{1}{9}$ .

\frac{2}{9} x

$\frac{2}{9} x$

Step 3.2

Combine

\frac{2}{9}

$\frac{2}{9}$ and

x

$x$ .

\frac{2 x}{9}

$\frac{2 x}{9}$

\frac{2 x}{9}

$\frac{2 x}{9}$