Calculus Examples

$\sqrt{3 x^{2}}$

Step 1

Rewrite $\frac{d}{d x} [\sqrt{3 x^{2}}]$ as $\frac{d}{d x} [x \sqrt{3}]$ .

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Step 1.1

Reorder $3$ and $x^{2}$ .

$\frac{d}{d x} [\sqrt{x^{2} \cdot 3}]$

Step 1.2

Pull terms out from under the radical.

$\frac{d}{d x} [x \sqrt{3}]$

Step 2

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

$\sqrt{3} \frac{d}{d x} [x]$

Step 3

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

$\sqrt{3} \cdot 1$

Step 4

Multiply $\sqrt{3}$ by $1$ .

$\sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3}$

Decimal Form:

$1.73205080 \dots$