Calculus Examples

$5 x^{- 2}$

Step 1

Since $5$ is constant with respect to $x$ , the derivative of $5 x^{- 2}$ with respect to $x$ is $5 \frac{d}{d x} [x^{- 2}]$ .

$5 \frac{d}{d x} [x^{- 2}]$

Step 2

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

$5 (- 2 x^{- 3})$

Step 3

Multiply $- 2$ by $5$ .

$- 10 x^{- 3}$

Step 4

Simplify.

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Step 4.1

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

$- 10 \frac{1}{x^{3}}$

Step 4.2

Combine $- 10$ and $\frac{1}{x^{3}}$ .

$\frac{- 10}{x^{3}}$

Step 4.3

Move the negative in front of the fraction.

$- \frac{10}{x^{3}}$