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

Find the derivative of x^0.5ln(x)-1x

Answer

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

Step-by-step explanation

Problem

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

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

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

Unlock this step-by-step solution!

Answer

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

Main topic:

Differential calculus

Used formulas:

5. See formulas

Time to solve it:

0.29 seconds