Calculus Examples

$\frac{x^{5}}{10}$

Step 1

Since $\frac{1}{10}$ is constant with respect to $x$ , the derivative of $\frac{x^{5}}{10}$ with respect to $x$ is $\frac{1}{10} \frac{d}{d x} [x^{5}]$ .

$\frac{1}{10} \frac{d}{d x} [x^{5}]$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 5$ .

$\frac{1}{10} (5 x^{4})$

Step 3

Simplify terms.

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Step 3.1

Combine $5$ and $\frac{1}{10}$ .

$\frac{5}{10} x^{4}$

Step 3.2

Combine $\frac{5}{10}$ and $x^{4}$ .

$\frac{5 x^{4}}{10}$

Step 3.3

Cancel the common factor of $5$ and $10$ .

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Step 3.3.1

Factor $5$ out of $5 x^{4}$ .

$\frac{5 (x^{4})}{10}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $5$ out of $10$ .

$\frac{5 x^{4}}{5 \cdot 2}$

Step 3.3.2.2

Cancel the common factor.

$\frac{5 x^{4}}{5 \cdot 2}$

Step 3.3.2.3

Rewrite the expression.

$\frac{x^{4}}{2}$