Calculus Examples

$f (x) = \frac{2 \tan (x)}{x}$

Step 1

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

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

Step 2

Differentiate using the Quotient Rule which states that $\frac{d}{d x} [\frac{f (x)}{g (x)}]$ is $\frac{g (x) \frac{d}{d x} [f (x)] - f (x) \frac{d}{d x} [g (x)]}{{g (x)}^{2}}$ where $f (x) = \tan (x)$ and $g (x) = x$ .

$2 \frac{x \frac{d}{d x} [\tan (x)] - \tan (x) \frac{d}{d x} [x]}{x^{2}}$

Step 3

The derivative of $\tan (x)$ with respect to $x$ is $\sec^{2} (x)$ .

$2 \frac{x \sec^{2} (x) - \tan (x) \frac{d}{d x} [x]}{x^{2}}$

Step 4

Differentiate using the Power Rule.

Tap for more steps...

Step 4.1

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 1$ .

$2 \frac{x \sec^{2} (x) - \tan (x) \cdot 1}{x^{2}}$

Step 4.2

Combine fractions.

Tap for more steps...

Step 4.2.1

Multiply $- 1$ by $1$ .

$2 \frac{x \sec^{2} (x) - \tan (x)}{x^{2}}$

Step 4.2.2

Combine $2$ and $\frac{x \sec^{2} (x) - \tan (x)}{x^{2}}$ .

$\frac{2 (x \sec^{2} (x) - \tan (x))}{x^{2}}$