Calculus Examples

$\frac{1}{9} \cdot \arctan (x)$

Step 1

Since $\frac{1}{9}$ is constant with respect to $x$ , the derivative of $\frac{1}{9} \cdot \arctan (x)$ with respect to $x$ is $\frac{1}{9} \frac{d}{d x} [\arctan (x)]$ .

$\frac{1}{9} \frac{d}{d x} [\arctan (x)]$

Step 2

The derivative of $\arctan (x)$ with respect to $x$ is $\frac{1}{1 + x^{2}}$ .

$\frac{1}{9} \cdot \frac{1}{1 + x^{2}}$

Step 3

Multiply $\frac{1}{9}$ by $\frac{1}{1 + x^{2}}$ .

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

Step 4

Simplify.

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Step 4.1

Apply the distributive property.

$\frac{1}{9 \cdot 1 + 9 x^{2}}$

Step 4.2

Multiply $9$ by $1$ .

$\frac{1}{9 + 9 x^{2}}$

Step 4.3

Reorder terms.

$\frac{1}{9 x^{2} + 9}$

Step 4.4

Factor $9$ out of $9 x^{2} + 9$ .

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Step 4.4.1

Factor $9$ out of $9 x^{2}$ .

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

Step 4.4.2

Factor $9$ out of $9$ .

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

Step 4.4.3

Factor $9$ out of $9 (x^{2}) + 9 (1)$ .

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