Calculus Examples

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

Step 1

Since $\frac{1}{8}$ is constant with respect to $x$ , the derivative of $\frac{x^{2}}{8}$ with respect to $x$ is $\frac{1}{8} \frac{d}{d x} [x^{2}]$ .

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

Step 2

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

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

Step 3

Simplify terms.

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Step 3.1

Combine $2$ and $\frac{1}{8}$ .

$\frac{2}{8} x$

Step 3.2

Combine $\frac{2}{8}$ and $x$ .

$\frac{2 x}{8}$

Step 3.3

Cancel the common factor of $2$ and $8$ .

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Step 3.3.1

Factor $2$ out of $2 x$ .

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

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $2$ out of $8$ .

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

Step 3.3.2.2

Cancel the common factor.

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

Step 3.3.2.3

Rewrite the expression.

$\frac{x}{4}$