Calculus Examples

$\sqrt{\frac{1}{18}}$

Step 1

Apply the constant rule.

$\sqrt{\frac{1}{18}} x + C$

Step 2

Simplify the answer.

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Step 2.1

Rewrite $\sqrt{\frac{1}{18}} x + C$ as $\frac{\sqrt{1}}{\sqrt{18}} x + C$ .

$\frac{\sqrt{1}}{\sqrt{18}} x + C$

Step 2.2

Simplify.

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Step 2.2.1

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{18}} x + C$

Step 2.2.2

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 2.2.2.1

Factor $9$ out of $18$ .

$\frac{1}{\sqrt{9 (2)}} x + C$

Step 2.2.2.2

Rewrite $9$ as $3^{2}$ .

$\frac{1}{\sqrt{3^{2} \cdot 2}} x + C$

Step 2.2.3

Pull terms out from under the radical.

$\frac{1}{3 \sqrt{2}} x + C$