Find the Derivative - d/dx 300/x

$\frac{300}{x}$

Step 1

Since $300$ is constant with respect to $x$ , the derivative of $\frac{300}{x}$ with respect to $x$ is $300 \frac{d}{d x} [\frac{1}{x}]$ .

$300 \frac{d}{d x} [\frac{1}{x}]$

Step 2

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

$300 \frac{d}{d x} [x^{- 1}]$

Step 3

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

$300 (- x^{- 2})$

Step 4

Multiply $- 1$ by $300$ .

$- 300 x^{- 2}$

Step 5

Simplify.

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

$- 300 \frac{1}{x^{2}}$

Combine terms.

Combine $- 300$ and $\frac{1}{x^{2}}$ .

$\frac{- 300}{x^{2}}$

Move the negative in front of the fraction.

$- \frac{300}{x^{2}}$