Calculus Examples

$\frac{x^{3}}{7}$

Step 1

Since $\frac{1}{7}$ is constant with respect to $x$ , the derivative of $\frac{x^{3}}{7}$ with respect to $x$ is $\frac{1}{7} \frac{d}{d x} [x^{3}]$ .

$\frac{1}{7} \frac{d}{d x} [x^{3}]$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 3$ .

$\frac{1}{7} (3 x^{2})$

Step 3

Combine fractions.

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Step 3.1

Combine $3$ and $\frac{1}{7}$ .

$\frac{3}{7} x^{2}$

Step 3.2

Combine $\frac{3}{7}$ and $x^{2}$ .

$\frac{3 x^{2}}{7}$