Calculus Examples

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

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to $\frac{x}{2}$ .

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

Step 1.2

Raise $2$ to the power of $2$ .

$\frac{d}{d x} [\frac{x^{2}}{4}]$

Step 2

Since $\frac{1}{4}$ is constant with respect to $x$ , the derivative of $\frac{x^{2}}{4}$ with respect to $x$ is $\frac{1}{4} \frac{d}{d x} [x^{2}]$ .

$\frac{1}{4} \frac{d}{d x} [x^{2}]$

Step 3

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

$\frac{1}{4} (2 x)$

Step 4

Simplify terms.

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Step 4.1

Combine $2$ and $\frac{1}{4}$ .

$\frac{2}{4} x$

Step 4.2

Combine $\frac{2}{4}$ and $x$ .

$\frac{2 x}{4}$

Step 4.3

Cancel the common factor of $2$ and $4$ .

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Step 4.3.1

Factor $2$ out of $2 x$ .

$\frac{2 (x)}{4}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $2$ out of $4$ .

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

Step 4.3.2.2

Cancel the common factor.

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

Step 4.3.2.3

Rewrite the expression.

$\frac{x}{2}$