Calculus Examples

$y = \frac{x^{7}}{7}$

Step 1

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

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

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 7$ .

$\frac{1}{7} (7 x^{6})$

Step 3

Simplify terms.

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Step 3.1

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

$\frac{7}{7} x^{6}$

Step 3.2

Combine $\frac{7}{7}$ and $x^{6}$ .

$\frac{7 x^{6}}{7}$

Step 3.3

Cancel the common factor of $7$ .

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Step 3.3.1

Cancel the common factor.

$\frac{7 x^{6}}{7}$

Step 3.3.2

Divide $x^{6}$ by $1$ .

$x^{6}$