Calculus Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Pull terms out from under the radical.

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

Step 2

Since $\frac{\sqrt{3}}{2}$ is constant with respect to $x$ , the derivative of $\frac{x \sqrt{3}}{2}$ with respect to $x$ is $\frac{\sqrt{3}}{2} \frac{d}{d x} [x]$ .

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

Step 3

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

$\frac{\sqrt{3}}{2} \cdot 1$

Step 4

Multiply $\frac{\sqrt{3}}{2}$ by $1$ .

$\frac{\sqrt{3}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{3}}{2}$

Decimal Form:

$0.86602540 \dots$