Calculus Examples

f (x) = 4 - | 0 |

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

Step 1

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

0

$0$ and

0

$0$ is

0

$0$ .

\frac{d}{d x} [4 - 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

$4 - 0$ with respect to

x

$x$ is

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

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

\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

$4$ is constant with respect to

x

$x$ , the derivative of

4

$4$ with respect to

x

$x$ is

0

$0$ .

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

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

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

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

Step 3

Evaluate

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

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

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Step 3.1

Multiply

- 1

$- 1$ by

0

$0$ .

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

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

Step 3.2

Since

0

$0$ is constant with respect to

x

$x$ , the derivative of

0

$0$ with respect to

x

$x$ is

0

$0$ .

0 + 0

$0 + 0$

0 + 0

$0 + 0$

Step 4

Add

0

$0$ and

0

$0$ .

0

$0$