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

Move the negative in front of the fraction.

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