Calculus Examples

$f (x) = x^{2} + x - 3$

Step 1

By the Sum Rule, the derivative of $x^{2} + x - 3$ with respect to $x$ is $\frac{d}{d x} [x^{2}] + \frac{d}{d x} [x] + \frac{d}{d x} [- 3]$ .

$\frac{d}{d x} [x^{2}] + \frac{d}{d x} [x] + \frac{d}{d x} [- 3]$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 2$ .

$2 x + \frac{d}{d x} [x] + \frac{d}{d x} [- 3]$

Step 3

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 1$ .

$2 x + 1 + \frac{d}{d x} [- 3]$

Step 4

Since $- 3$ is constant with respect to $x$ , the derivative of $- 3$ with respect to $x$ is $0$ .

$2 x + 1 + 0$

Step 5

Add $2 x + 1$ and $0$ .

$2 x + 1$