Calculus Examples

$\frac{d}{d x} (x + 5)$

Step 1

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

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

Step 2

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

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

Step 3

Since $5$ is constant with respect to $x$ , the derivative of $5$ with respect to $x$ is $0$ .

$1 + 0$

Step 4

Add $1$ and $0$ .

$1$