Calculus Examples

$\frac{\cot (x)}{\cos (x)}$

Step 1

Rewrite $\cot (x)$ in terms of sines and cosines.

$\frac{d}{d x} [\frac{\frac{\cos (x)}{\sin (x)}}{\cos (x)}]$

Step 2

Rewrite $\frac{\frac{\cos (x)}{\sin (x)}}{\cos (x)}$ as a product.

$\frac{d}{d x} [\frac{\cos (x)}{\sin (x)} \cdot \frac{1}{\cos (x)}]$

Step 3

Cancel the common factor of $\cos (x)$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

$\frac{d}{d x} [\frac{\cos (x)}{\sin (x)} \cdot \frac{1}{\cos (x)}]$

Step 3.2

Rewrite the expression.

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

Step 4

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

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

Step 5

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

$- \csc (x) \cot (x)$

Step 6

Reorder the factors of $- \csc (x) \cot (x)$ .

$- \cot (x) \csc (x)$