Calculus Examples

x^{2} - 9

$x^{2} - 9$

Step 1

By the Sum Rule, the derivative of

x^{2} - 9

$x^{2} - 9$ with respect to

x

$x$ is

\frac{d}{d x} [x^{2}] + \frac{d}{d x} [- 9]

$\frac{d}{d x} [x^{2}] + \frac{d}{d x} [- 9]$ .

\frac{d}{d x} [x^{2}] + \frac{d}{d x} [- 9]

$\frac{d}{d x} [x^{2}] + \frac{d}{d x} [- 9]$

Step 2

Differentiate using the Power Rule which states that

\frac{d}{d x} [x^{n}]

$\frac{d}{d x} [x^{n}]$ is

n x^{n - 1}

$n x^{n - 1}$ where

n = 2

$n = 2$ .

2 x + \frac{d}{d x} [- 9]

$2 x + \frac{d}{d x} [- 9]$

Step 3

Since

- 9

$- 9$ is constant with respect to

x

$x$ , the derivative of

- 9

$- 9$ with respect to

x

$x$ is

0

$0$ .

2 x + 0

$2 x + 0$

Step 4

Add

2 x

$2 x$ and

0

$0$ .

2 x

$2 x$

x^{2} - 9

$x^{2} - 9$

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