Calculus Examples

$g (x) = \frac{12 (\sqrt{4} - 3)}{4 - 9}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $4$ as $2^{2}$ .

$\frac{d}{d x} [\frac{12 (\sqrt{2^{2}} - 3)}{4 - 9}]$

Step 1.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{d}{d x} [\frac{12 (2 - 3)}{4 - 9}]$

Step 1.3

Subtract $3$ from $2$ .

$\frac{d}{d x} [\frac{12 \cdot - 1}{4 - 9}]$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Subtract $9$ from $4$ .

$\frac{d}{d x} [\frac{12 \cdot - 1}{- 5}]$

Step 2.2

Multiply $12$ by $- 1$ .

$\frac{d}{d x} [\frac{- 12}{- 5}]$

Step 2.3

Dividing two negative values results in a positive value.

$\frac{d}{d x} [\frac{12}{5}]$

Step 3

Since $\frac{12}{5}$ is constant with respect to $x$ , the derivative of $\frac{12}{5}$ with respect to $x$ is $0$ .

$0$