Calculus Examples

$\frac{1}{\tan (x)}$

Step 1

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

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

Step 2

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (x)}{\cos (x)}$ .

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

Step 3

Convert from $\frac{\cos (x)}{\sin (x)}$ to $\cot (x)$ .

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

Step 4

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

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