Calculus Examples

$\frac{6}{x^{2}}$

Step 1

This derivative could not be completed using the chain rule. Mathway will use another method.

Step 2

Since $6$ is constant with respect to $x$ , the derivative of $\frac{6}{x^{2}}$ with respect to $x$ is $6 \frac{d}{d x} [\frac{1}{x^{2}}]$ .

$6 \frac{d}{d x} [\frac{1}{x^{2}}]$

Step 3

Apply basic rules of exponents.

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Step 3.1

Rewrite $\frac{1}{x^{2}}$ as ${(x^{2})}^{- 1}$ .

$6 \frac{d}{d x} [{(x^{2})}^{- 1}]$

Step 3.2

Multiply the exponents in ${(x^{2})}^{- 1}$ .

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Step 3.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$6 \frac{d}{d x} [x^{2 \cdot - 1}]$

Step 3.2.2

Multiply $2$ by $- 1$ .

$6 \frac{d}{d x} [x^{- 2}]$

Step 4

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = - 2$ .

$6 (- 2 x^{- 3})$

Step 5

Multiply $- 2$ by $6$ .

$- 12 x^{- 3}$

Step 6

Simplify.

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Step 6.1

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

$- 12 \frac{1}{x^{3}}$

Step 6.2

Combine terms.

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Step 6.2.1

Combine $- 12$ and $\frac{1}{x^{3}}$ .

$\frac{- 12}{x^{3}}$

Step 6.2.2

Move the negative in front of the fraction.

$- \frac{12}{x^{3}}$