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x/ln(x)
The derivative of the function/ x/ln(x)

Derivative of x/ln(x)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  x   
------
log(x)
xlog⁡(x)\frac{x}{\log{\left(x \right)}} 
x/log(x)
Detail solution

  1. Apply the quotient rule, which is:

    ddxf(x)g(x)=−f(x)ddxg(x)+g(x)ddxf(x)g2(x)\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}

    f(x)=xf{\left(x \right)} = x and g(x)=log⁡(x)g{\left(x \right)} = \log{\left(x \right)}.

    To find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Apply the power rule: xx goes to 11

    To find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. The derivative of log⁡(x)\log{\left(x \right)} is 1x\frac{1}{x}.

    Now plug in to the quotient rule:

    log⁡(x)−1log⁡(x)2\frac{\log{\left(x \right)} - 1}{\log{\left(x \right)}^{2}}

The answer is:

log⁡(x)−1log⁡(x)2\frac{\log{\left(x \right)} - 1}{\log{\left(x \right)}^{2}}

The graph
02468-8-6-4-2-1010-200100
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  1         1   
------ - -------
log(x)      2   
         log (x)
1log⁡(x)−1log⁡(x)2\frac{1}{\log{\left(x \right)}} - \frac{1}{\log{\left(x \right)}^{2}}
Simplify
The second derivative [src] 
       2   
-1 + ------
     log(x)
-----------
      2    
 x*log (x)
−1+2log⁡(x)xlog⁡(x)2\frac{-1 + \frac{2}{\log{\left(x \right)}}}{x \log{\left(x \right)}^{2}}
Simplify
The third derivative [src] 
       6   
1 - -------
       2   
    log (x)
-----------
  2    2   
 x *log (x)
1−6log⁡(x)2x2log⁡(x)2\frac{1 - \frac{6}{\log{\left(x \right)}^{2}}}{x^{2} \log{\left(x \right)}^{2}}
Simplify
The graph
Derivative of x/ln(x)
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