Calculus Examples

x^{2} + 2 x

$x^{2} + 2 x$

Step 1

Differentiate.

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Step 1.1

By the Sum Rule, the derivative of

x^{2} + 2 x

$x^{2} + 2 x$ with respect to

x

$x$ is

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

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

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

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

Step 1.2

Differentiate using the Power Rule which states that

\frac{d}{d x} [x^{n}]

$\frac{d}{d x} [x^{n}]$ is

n x^{n - 1}

$n x^{n - 1}$ where

n = 2

$n = 2$ .

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

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

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

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

Step 2

Evaluate

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

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

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Step 2.1

Since

2

$2$ is constant with respect to

x

$x$ , the derivative of

2 x

$2 x$ with respect to

x

$x$ is

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

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

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

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

Step 2.2

Differentiate using the Power Rule which states that

\frac{d}{d x} [x^{n}]

$\frac{d}{d x} [x^{n}]$ is

n x^{n - 1}

$n x^{n - 1}$ where

n = 1

$n = 1$ .

2 x + 2 \cdot 1

$2 x + 2 \cdot 1$

Step 2.3

Multiply

2

$2$ by

1

$1$ .

2 x + 2

$2 x + 2$

2 x + 2

$2 x + 2$