Calculus Examples

\frac{3}{x}

$\frac{3}{x}$

Step 1

Since

3

$3$ is constant with respect to

x

$x$ , the derivative of

\frac{3}{x}

$\frac{3}{x}$ with respect to

x

$x$ is

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

$3 \frac{d}{d x} [\frac{1}{x}]$ .

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

$3 \frac{d}{d x} [\frac{1}{x}]$

Step 2

Rewrite

\frac{1}{x}

$\frac{1}{x}$ as

x^{- 1}

$x^{- 1}$ .

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

$3 \frac{d}{d x} [x^{- 1}]$

Step 3

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

$n = - 1$ .

3 (- x^{- 2})

$3 (- x^{- 2})$

Step 4

Multiply

- 1

$- 1$ by

3

$3$ .

- 3 x^{- 2}

$- 3 x^{- 2}$

Step 5

Simplify.

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Step 5.1

Rewrite the expression using the negative exponent rule

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

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

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

$- 3 \frac{1}{x^{2}}$

Step 5.2

Combine terms.

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Step 5.2.1

Combine

- 3

$- 3$ and

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

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

\frac{- 3}{x^{2}}

$\frac{- 3}{x^{2}}$

Step 5.2.2

Move the negative in front of the fraction.

- \frac{3}{x^{2}}

$- \frac{3}{x^{2}}$

- \frac{3}{x^{2}}

$- \frac{3}{x^{2}}$

- \frac{3}{x^{2}}

$- \frac{3}{x^{2}}$