Calculus Examples

$f (x) = \frac{1}{2} x^{2}$

Step 1

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

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

Step 2

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

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

Step 3

Simplify terms.

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Step 3.1

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

$\frac{2}{2} x$

Step 3.2

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

$\frac{2 x}{2}$

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Cancel the common factor.

$\frac{2 x}{2}$

Step 3.3.2

Divide $x$ by $1$ .

$x$