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# Find the derivative using the constant rule [x]

### Videos

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

## Step-by-step explanation

Problem to solve:

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

The derivative of a sum of two functions is the sum of the derivatives of each function

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

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

### Main topic:

Differential calculus

~ 0.58 seconds