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# Derive the function ln((xe^(2x))^0.5) with respect to x

### Videos

$\frac{\frac{1}{2}e^x+e^x\cdot x}{e^x\cdot x}$

## Step-by-step explanation

Problem

$\frac{d}{dx}\left(\ln\left(\sqrt{x e^{2x}}\right)\right)$
1

The power of a product is equal to the product of it's factors raised to the same power

$\frac{d}{dx}\left(\ln\left(e^x\sqrt{x}\right)\right)$

$\frac{\frac{1}{2}e^x+e^x\cdot x}{e^x\cdot x}$

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$\frac{d}{dx}\left(\ln\left(\sqrt{x e^{2x}}\right)\right)$

### Main topic:

Differential calculus

~ 1.12 seconds