Calculus Examples

$\frac{5}{5 x}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $5$ .

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Step 1.1.1

Cancel the common factor.

$\frac{d}{d x} [\frac{5}{5 x}]$

Step 1.1.2

Rewrite the expression.

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

Step 1.2

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

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

Step 2

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

$- x^{- 2}$

Step 3

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

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