Calculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

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

Step 5

The derivative of $\sec (x)$ with respect to $x$ is $\sec (x) \tan (x)$ .

$\sec (x) \tan (x)$