Calculus Examples

$\frac{2 x + 5}{3}$

Step 1

Since $\frac{1}{3}$ is constant with respect to $x$ , the derivative of $\frac{2 x + 5}{3}$ with respect to $x$ is $\frac{1}{3} \frac{d}{d x} [2 x + 5]$ .

$\frac{1}{3} \frac{d}{d x} [2 x + 5]$

Step 2

By the Sum Rule, the derivative of $2 x + 5$ with respect to $x$ is $\frac{d}{d x} [2 x] + \frac{d}{d x} [5]$ .

$\frac{1}{3} (\frac{d}{d x} [2 x] + \frac{d}{d x} [5])$

Step 3

Since $2$ is constant with respect to $x$ , the derivative of $2 x$ with respect to $x$ is $2 \frac{d}{d x} [x]$ .

$\frac{1}{3} (2 \frac{d}{d x} [x] + \frac{d}{d x} [5])$

Step 4

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

$\frac{1}{3} (2 \cdot 1 + \frac{d}{d x} [5])$

Step 5

Multiply $2$ by $1$ .

$\frac{1}{3} (2 + \frac{d}{d x} [5])$

Step 6

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

$\frac{1}{3} (2 + 0)$

Step 7

Combine fractions.

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Step 7.1

Add $2$ and $0$ .

$\frac{1}{3} \cdot 2$

Step 7.2

Combine $\frac{1}{3}$ and $2$ .

$\frac{2}{3}$