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

Find the derivative of 1/(xln(x))

Answer

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

Step-by-step explanation

Problem

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

Applying the quotient rule which states that if $f(x)$ and $g(x)$ are functions and $h(x)$ is the function defined by ${\displaystyle h(x) = \frac{f(x)}{g(x)}}$, where ${g(x) \neq 0}$, then ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$

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

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Answer

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

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

Main topic:

Differential calculus

Used formulas:

5. See formulas

Time to solve it:

~ 0.36 seconds