Calculus Examples

$\frac{- 4}{x}$

Step 1

Move the negative in front of the fraction.

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

Step 2

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 3

Rewrite $\frac{1}{x}$ as $x^{- 1}$ .

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

Step 4

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 5

Multiply $- 1$ by $- 4$ .

$4 x^{- 2}$

Step 6

Simplify.

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Step 6.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 6.2

Combine $4$ and $\frac{1}{x^{2}}$ .

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