Calculus Examples

$\csc (x) + \cot (x)$

Step 1

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

$\frac{d}{d x} [\csc (x)] + \frac{d}{d x} [\cot (x)]$

Step 2

The derivative of $\csc (x)$ with respect to $x$ is $- \csc (x) \cot (x)$ .

$- \csc (x) \cot (x) + \frac{d}{d x} [\cot (x)]$

Step 3

The derivative of $\cot (x)$ with respect to $x$ is $- \csc^{2} (x)$ .

$- \csc (x) \cot (x) - \csc^{2} (x)$

Step 4

Reorder terms.

$- \cot (x) \csc (x) - \csc^{2} (x)$