Calculus Examples

$y = x^{2} + x$ , $x = 2$

Step 1

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

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

Step 2

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

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

Step 3

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

$2 x + 1$

Step 4

Evaluate the derivative at $x = 2$ .

$2 (2) + 1$

Step 5

Simplify.

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Step 5.1

Multiply $2$ by $2$ .

$4 + 1$

Step 5.2

Add $4$ and $1$ .

$5$

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