Calculus Examples

$5 \arctan (x)$

Step 1

Since $5$ is constant with respect to $x$ , the derivative of $5 \arctan (x)$ with respect to $x$ is $5 \frac{d}{d x} [\arctan (x)]$ .

$5 \frac{d}{d x} [\arctan (x)]$

Step 2

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

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

Step 3

Combine fractions.

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Step 3.1

Combine $5$ and $\frac{1}{1 + x^{2}}$ .

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

Step 3.2

Reorder terms.

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