Calculus Examples

$f (x) = (5 x - 1)$

Step 1

By the Sum Rule, the derivative of $5 x - 1$ with respect to $x$ is $\frac{d}{d x} [5 x] + \frac{d}{d x} [- 1]$ .

$\frac{d}{d x} [5 x] + \frac{d}{d x} [- 1]$

Step 2

Since $5$ is constant with respect to $x$ , the derivative of $5 x$ with respect to $x$ is $5 \frac{d}{d x} [x]$ .

$5 \frac{d}{d x} [x] + \frac{d}{d x} [- 1]$

Step 3

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

$5 \cdot 1 + \frac{d}{d x} [- 1]$

Step 4

Multiply $5$ by $1$ .

$5 + \frac{d}{d x} [- 1]$

Step 5

Since $- 1$ is constant with respect to $x$ , the derivative of $- 1$ with respect to $x$ is $0$ .

$5 + 0$

Step 6

Add $5$ and $0$ .

$5$