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x^2/log(x)
The derivative of the function/ x^2/log(x)

Derivative of x^2/log(x)

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

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from to

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The solution

You have entered [src] 
   2  
  x   
------
log(x)
x2log⁡(x)\frac{x^{2}}{\log{\left(x \right)}} 
x^2/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)=x2f{\left(x \right)} = x^{2} 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: x2x^{2} goes to 2x2 x

    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:

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

  2. Now simplify:

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

The answer is:

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

The graph
02468-8-6-4-2-1010-200200
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     x       2*x  
- ------- + ------
     2      log(x)
  log (x)
2xlog⁡(x)−xlog⁡(x)2\frac{2 x}{\log{\left(x \right)}} - \frac{x}{\log{\left(x \right)}^{2}}
Simplify
The second derivative [src] 
                   2   
             1 + ------
      4          log(x)
2 - ------ + ----------
    log(x)     log(x)  
-----------------------
         log(x)
1+2log⁡(x)log⁡(x)+2−4log⁡(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)}}
Simplify
The third derivative [src] 
  /        3        3   \
2*|-1 - ------- + ------|
  |        2      log(x)|
  \     log (x)         /
-------------------------
             2           
        x*log (x)
2(−1+3log⁡(x)−3log⁡(x)2)xlog⁡(x)2\frac{2 \left(-1 + \frac{3}{\log{\left(x \right)}} - \frac{3}{\log{\left(x \right)}^{2}}\right)}{x \log{\left(x \right)}^{2}}
Simplify
The graph
Derivative of x^2/log(x)
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