Mister Exam

Other calculators

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

Derivative of x/log(x)

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

The graph:

from to

Piecewise:

The solution

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

  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Apply the power rule: goes to

    To find :

    1. The derivative of is .

    Now plug in to the quotient rule:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  1         1   
------ - -------
log(x)      2   
         log (x)
$$\frac{1}{\log{\left(x \right)}} - \frac{1}{\log{\left(x \right)}^{2}}$$
Simplify
The second derivative [src] 
       2   
-1 + ------
     log(x)
-----------
      2    
 x*log (x)
$$\frac{-1 + \frac{2}{\log{\left(x \right)}}}{x \log{\left(x \right)}^{2}}$$
Simplify
The third derivative [src] 
       6   
1 - -------
       2   
    log (x)
-----------
  2    2   
 x *log (x)
$$\frac{1 - \frac{6}{\log{\left(x \right)}^{2}}}{x^{2} \log{\left(x \right)}^{2}}$$
Simplify
The graph
Derivative of x/log(x)
    © Mister Exam – Calculator