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x^2/log(x)

Derivative of x^2/log(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   2  
  x   
------
log(x)
$$\frac{x^{2}}{\log{\left(x \right)}}$$
x^2/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:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
     x       2*x  
- ------- + ------
     2      log(x)
  log (x)         
$$\frac{2 x}{\log{\left(x \right)}} - \frac{x}{\log{\left(x \right)}^{2}}$$
The second derivative [src]
                   2   
             1 + ------
      4          log(x)
2 - ------ + ----------
    log(x)     log(x)  
-----------------------
         log(x)        
$$\frac{\frac{1 + \frac{2}{\log{\left(x \right)}}}{\log{\left(x \right)}} + 2 - \frac{4}{\log{\left(x \right)}}}{\log{\left(x \right)}}$$
The third derivative [src]
  /        3        3   \
2*|-1 - ------- + ------|
  |        2      log(x)|
  \     log (x)         /
-------------------------
             2           
        x*log (x)        
$$\frac{2 \left(-1 + \frac{3}{\log{\left(x \right)}} - \frac{3}{\log{\left(x \right)}^{2}}\right)}{x \log{\left(x \right)}^{2}}$$
The graph
Derivative of x^2/log(x)