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# Find the derivative of x^0.5ln(x)

### Videos

$\frac{1+\frac{1}{2}\ln\left(x\right)}{\sqrt{x}}$

## Step-by-step explanation

Problem

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

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\sqrt{x}$ and $g=\ln\left(x\right)$

$\sqrt{x}\cdot\frac{d}{dx}\left(\ln\left(x\right)\right)+\ln\left(x\right)\frac{d}{dx}\left(\sqrt{x}\right)$

$\frac{1+\frac{1}{2}\ln\left(x\right)}{\sqrt{x}}$

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

### Main topic:

Differential calculus

~ 0.69 seconds