Calculus Examples

$y = \frac{x^{2} + 2 x}{x}$

Step 1

Simplify terms.

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Step 1.1

Factor $x$ out of $x^{2} + 2 x$ .

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Step 1.1.1

Factor $x$ out of $x^{2}$ .

$\frac{d}{d x} [\frac{x \cdot x + 2 x}{x}]$

Step 1.1.2

Factor $x$ out of $2 x$ .

$\frac{d}{d x} [\frac{x \cdot x + x \cdot 2}{x}]$

Step 1.1.3

Factor $x$ out of $x \cdot x + x \cdot 2$ .

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

Step 1.2

Cancel the common factor of $x$ .

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Step 1.2.1

Cancel the common factor.

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

Step 1.2.2

Divide $x + 2$ by $1$ .

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

Step 2

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

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

Step 3

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

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

Step 4

Since $2$ is constant with respect to $x$ , the derivative of $2$ with respect to $x$ is $0$ .

$1 + 0$

Step 5

Add $1$ and $0$ .

$1$