Calculus Examples

f (x) = \frac{1}{x}

$f (x) = \frac{1}{x}$

Step 1

Rewrite

\frac{1}{x}

$\frac{1}{x}$ as

x^{- 1}

$x^{- 1}$ .

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

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

Step 2

Differentiate using the Power Rule which states that

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

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

n x^{n - 1}

$n x^{n - 1}$ where

n = - 1

$n = - 1$ .

- x^{- 2}

$- x^{- 2}$

Step 3

Rewrite the expression using the negative exponent rule

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

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

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

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

f (x) = \frac{1}{x}

$f (x) = \frac{1}{x}$

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