Calculus Examples

$y = 8 x^{- 5}$

Step 1

Since $8$ is constant with respect to $x$ , the derivative of $8 x^{- 5}$ with respect to $x$ is $8 \frac{d}{d x} [x^{- 5}]$ .

$8 \frac{d}{d x} [x^{- 5}]$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = - 5$ .

$8 (- 5 x^{- 6})$

Step 3

Multiply $- 5$ by $8$ .

$- 40 x^{- 6}$

Step 4

Simplify.

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Step 4.1

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

$- 40 \frac{1}{x^{6}}$

Step 4.2

Combine $- 40$ and $\frac{1}{x^{6}}$ .

$\frac{- 40}{x^{6}}$

Step 4.3

Move the negative in front of the fraction.

$- \frac{40}{x^{6}}$