Find the Derivative - d/d@VAR f(x)=x^2-3x+18

$f (x) = x^{2} - 3 x + 18$

Step 1

Differentiate.

By the Sum Rule, the derivative of $x^{2} - 3 x + 18$ with respect to $x$ is $\frac{d}{d x} [x^{2}] + \frac{d}{d x} [- 3 x] + \frac{d}{d x} [18]$ .

$\frac{d}{d x} [x^{2}] + \frac{d}{d x} [- 3 x] + \frac{d}{d x} [18]$

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

$2 x + \frac{d}{d x} [- 3 x] + \frac{d}{d x} [18]$

Step 2

Evaluate $\frac{d}{d x} [- 3 x]$ .

Since $- 3$ is constant with respect to $x$ , the derivative of $- 3 x$ with respect to $x$ is $- 3 \frac{d}{d x} [x]$ .

$2 x - 3 \frac{d}{d x} [x] + \frac{d}{d x} [18]$

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

$2 x - 3 \cdot 1 + \frac{d}{d x} [18]$

Multiply $- 3$ by $1$ .

$2 x - 3 + \frac{d}{d x} [18]$

Step 3

Differentiate using the Constant Rule.

Since $18$ is constant with respect to $x$ , the derivative of $18$ with respect to $x$ is $0$ .

$2 x - 3 + 0$

Add $2 x - 3$ and $0$ .

$2 x - 3$