Calculus Examples

$\frac{2 \csc (x)}{\sec (x)}$

Step 1

Since $2$ is constant with respect to $x$ , the derivative of $\frac{2 \csc (x)}{\sec (x)}$ with respect to $x$ is $2 \frac{d}{d x} [\frac{\csc (x)}{\sec (x)}]$ .

$2 \frac{d}{d x} [\frac{\csc (x)}{\sec (x)}]$

Step 2

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

$2 \frac{d}{d x} [\frac{\csc (x)}{\frac{1}{\cos (x)}}]$

Step 3

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

$2 \frac{d}{d x} [\frac{\frac{1}{\sin (x)}}{\frac{1}{\cos (x)}}]$

Step 4

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\cos (x)}$ .

$2 \frac{d}{d x} [\frac{\cos (x)}{\sin (x)}]$

Step 5

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

$2 \frac{d}{d x} [\cot (x)]$

Step 6

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

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

Step 7

Multiply $- 1$ by $2$ .

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