Calculus Examples

$f (x) = 4800 {(20)}^{- 3}$

Step 1

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

$\frac{d}{d x} [4800 \frac{1}{20^{3}}]$

Step 2

Simplify terms.

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Step 2.1

Raise $20$ to the power of $3$ .

$\frac{d}{d x} [4800 (\frac{1}{8000})]$

Step 2.2

Combine $4800$ and $\frac{1}{8000}$ .

$\frac{d}{d x} [\frac{4800}{8000}]$

Step 2.3

Cancel the common factor of $4800$ and $8000$ .

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Step 2.3.1

Factor $1600$ out of $4800$ .

$\frac{d}{d x} [\frac{1600 (3)}{8000}]$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $1600$ out of $8000$ .

$\frac{d}{d x} [\frac{1600 \cdot 3}{1600 \cdot 5}]$

Step 2.3.2.2

Cancel the common factor.

$\frac{d}{d x} [\frac{1600 \cdot 3}{1600 \cdot 5}]$

Step 2.3.2.3

Rewrite the expression.

$\frac{d}{d x} [\frac{3}{5}]$

Step 3

Since $\frac{3}{5}$ is constant with respect to $x$ , the derivative of $\frac{3}{5}$ with respect to $x$ is $0$ .

$0$