Calculus Examples

$\frac{2 x^{2}}{5}$

Step 1

Since $\frac{2}{5}$ is constant with respect to $x$ , the derivative of $\frac{2 x^{2}}{5}$ with respect to $x$ is $\frac{2}{5} \frac{d}{d x} [x^{2}]$ .

$\frac{2}{5} \frac{d}{d x} [x^{2}]$

Step 2

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

$\frac{2}{5} (2 x)$

Step 3

Combine fractions.

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Step 3.1

Combine $2$ and $\frac{2}{5}$ .

$\frac{2 \cdot 2}{5} x$

Step 3.2

Multiply $2$ by $2$ .

$\frac{4}{5} x$

Step 3.3

Combine $\frac{4}{5}$ and $x$ .

$\frac{4 x}{5}$