Calculus Examples

$f (x) = 4 - | 0 |$

Step 1

The absolute value is the distance between a number and zero. The distance between $0$ and $0$ is $0$ .

$\frac{d}{d x} [4 - 0]$

Step 2

Differentiate.

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Step 2.1

By the Sum Rule, the derivative of $4 - 0$ with respect to $x$ is $\frac{d}{d x} [4] + \frac{d}{d x} [- 0]$ .

$\frac{d}{d x} [4] + \frac{d}{d x} [- 0]$

Step 2.2

Since $4$ is constant with respect to $x$ , the derivative of $4$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [- 0]$

Step 3

Evaluate $\frac{d}{d x} [- 0]$ .

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Step 3.1

Multiply $- 1$ by $0$ .

$0 + \frac{d}{d x} [0]$

Step 3.2

Since $0$ is constant with respect to $x$ , the derivative of $0$ with respect to $x$ is $0$ .

$0 + 0$

Step 4

Add $0$ and $0$ .

$0$