Calculus Examples

$(\frac{1}{3}) x^{6}$

Step 1

Combine $\frac{1}{3}$ and $x^{6}$ .

$\frac{d}{d x} [\frac{x^{6}}{3}]$

Step 2

Since $\frac{1}{3}$ is constant with respect to $x$ , the derivative of $\frac{x^{6}}{3}$ with respect to $x$ is $\frac{1}{3} \frac{d}{d x} [x^{6}]$ .

$\frac{1}{3} \frac{d}{d x} [x^{6}]$

Step 3

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 6$ .

$\frac{1}{3} (6 x^{5})$

Step 4

Simplify terms.

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Step 4.1

Combine $6$ and $\frac{1}{3}$ .

$\frac{6}{3} x^{5}$

Step 4.2

Combine $\frac{6}{3}$ and $x^{5}$ .

$\frac{6 x^{5}}{3}$

Step 4.3

Cancel the common factor of $6$ and $3$ .

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Step 4.3.1

Factor $3$ out of $6 x^{5}$ .

$\frac{3 (2 x^{5})}{3}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $3$ out of $3$ .

$\frac{3 (2 x^{5})}{3 (1)}$

Step 4.3.2.2

Cancel the common factor.

$\frac{3 (2 x^{5})}{3 \cdot 1}$

Step 4.3.2.3

Rewrite the expression.

$\frac{2 x^{5}}{1}$

Step 4.3.2.4

Divide $2 x^{5}$ by $1$ .

$2 x^{5}$