Calculus Examples

$f (x) = \arctan (x) + arccot (x)$

Step 1

By the Sum Rule, the derivative of $\arctan (x) + arccot (x)$ with respect to $x$ is $\frac{d}{d x} [\arctan (x)] + \frac{d}{d x} [arccot (x)]$ .

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

Step 2

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

$\frac{1}{1 + x^{2}} + \frac{d}{d x} [arccot (x)]$

Step 3

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

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

Step 4

Subtract $\frac{1}{1 + x^{2}}$ from $\frac{1}{1 + x^{2}}$ .

$0$