Calculus Examples

\frac{x^{2}}{8}

$\frac{x^{2}}{8}$

Step 1

Since

\frac{1}{8}

$\frac{1}{8}$ is constant with respect to

x

$x$ , the derivative of

\frac{x^{2}}{8}

$\frac{x^{2}}{8}$ with respect to

x

$x$ is

\frac{1}{8} \frac{d}{d x} [x^{2}]

$\frac{1}{8} \frac{d}{d x} [x^{2}]$ .

\frac{1}{8} \frac{d}{d x} [x^{2}]

$\frac{1}{8} \frac{d}{d x} [x^{2}]$

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}{8} (2 x)

$\frac{1}{8} (2 x)$

Step 3

Simplify terms.

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Step 3.1

Combine

2

$2$ and

\frac{1}{8}

$\frac{1}{8}$ .

\frac{2}{8} x

$\frac{2}{8} x$

Step 3.2

Combine

\frac{2}{8}

$\frac{2}{8}$ and

x

$x$ .

\frac{2 x}{8}

$\frac{2 x}{8}$

Step 3.3

Cancel the common factor of

2

$2$ and

8

$8$ .

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Step 3.3.1

Factor

2

$2$ out of

2 x

$2 x$ .

\frac{2 (x)}{8}

$\frac{2 (x)}{8}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor

2

$2$ out of

8

$8$ .

\frac{2 x}{2 \cdot 4}

$\frac{2 x}{2 \cdot 4}$

Step 3.3.2.2

Cancel the common factor.

\frac{2 x}{2 \cdot 4}

$\frac{2 x}{2 \cdot 4}$

Step 3.3.2.3

Rewrite the expression.

\frac{x}{4}

$\frac{x}{4}$

\frac{x}{4}

$\frac{x}{4}$

\frac{x}{4}

$\frac{x}{4}$

\frac{x}{4}

$\frac{x}{4}$

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$