Calculus Examples

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

Step 1

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

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Step 1.1

Rewrite $e^{2 x}$ as ${(e^{x})}^{2}$ .

$\frac{d}{d x} [\sqrt{{(e^{x})}^{2}}]$

Step 1.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{d}{d x} [e^{x}]$

Step 2

Differentiate using the Exponential Rule which states that $\frac{d}{d x} [a^{x}]$ is $a^{x} \ln (a)$ where $a$ = $e$ .

$e^{x}$