Calculus Examples

$\frac{4}{x}$

Step 1

Since

$4$ is constant with respect to

$x$ , the derivative of

$\frac{4}{x}$ with respect to

$x$ is

$4 \frac{d}{d x} [\frac{1}{x}]$ .

$4 \frac{d}{d x} [\frac{1}{x}]$

Step 2

Rewrite

$\frac{1}{x}$ as

$x^{- 1}$ .

$4 \frac{d}{d x} [x^{- 1}]$

Step 3

Differentiate using the Power Rule which states that

$\frac{d}{d x} [x^{n}]$ is

$n x^{n - 1}$ where

$n = - 1$ .

$4 (- x^{- 2})$

Step 4

Multiply

$- 1$ by

$4$ .

$- 4 x^{- 2}$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Rewrite the expression using the negative exponent rule

$b^{- n} = \frac{1}{b^{n}}$ .

$- 4 \frac{1}{x^{2}}$

Step 5.2

Combine terms.

Tap for more steps...

Step 5.2.1

Combine

$- 4$ and

$\frac{1}{x^{2}}$ .

$\frac{- 4}{x^{2}}$

Step 5.2.2

Move the negative in front of the fraction.

$- \frac{4}{x^{2}}$