Calculus Examples

$x^{2} + 6 x$

Step 1

Differentiate.

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Step 1.1

By the Sum Rule, the derivative of $x^{2} + 6 x$ with respect to $x$ is $\frac{d}{d x} [x^{2}] + \frac{d}{d x} [6 x]$ .

$\frac{d}{d x} [x^{2}] + \frac{d}{d x} [6 x]$

Step 1.2

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

$2 x + \frac{d}{d x} [6 x]$

Step 2

Evaluate $\frac{d}{d x} [6 x]$ .

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Step 2.1

Since $6$ is constant with respect to $x$ , the derivative of $6 x$ with respect to $x$ is $6 \frac{d}{d x} [x]$ .

$2 x + 6 \frac{d}{d x} [x]$

Step 2.2

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

$2 x + 6 \cdot 1$

Step 2.3

Multiply $6$ by $1$ .

$2 x + 6$