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Derivative of:
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Derivative of x^2/log(x)
Derivative of log(x+2)
Limit of the function:
x^2/log(x)
Identical expressions
x^ two /log(x)
x squared divide by logarithm of (x)
x to the power of two divide by logarithm of (x)
x2/log(x)
x2/logx
x²/log(x)
x to the power of 2/log(x)
x^2/logx
x^2 divide by log(x)

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

Derivative of x^2/log(x)

The solution

You have entered [src]

   2  
  x   
------
log(x)

$$\frac{x^{2}}{\log{\left(x \right)}}$$

x^2/log(x)

Detail solution

Apply the quotient rule, which is:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = x^{2}$ and $g{\left(x \right)} = \log{\left(x \right)}$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{2}$ goes to $2 x$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
Now plug in to the quotient rule:

$\frac{2 x \log{\left(x \right)} - x}{\log{\left(x \right)}^{2}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     x       2*x  
- ------- + ------
     2      log(x)
  log (x)

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

Simplify

The second derivative [src]

                   2   
             1 + ------
      4          log(x)
2 - ------ + ----------
    log(x)     log(x)  
-----------------------
         log(x)

$$\frac{\frac{1 + \frac{2}{\log{\left(x \right)}}}{\log{\left(x \right)}} + 2 - \frac{4}{\log{\left(x \right)}}}{\log{\left(x \right)}}$$

Simplify

The third derivative [src]

  /        3        3   \
2*|-1 - ------- + ------|
  |        2      log(x)|
  \     log (x)         /
-------------------------
             2           
        x*log (x)

$$\frac{2 \left(-1 + \frac{3}{\log{\left(x \right)}} - \frac{3}{\log{\left(x \right)}^{2}}\right)}{x \log{\left(x \right)}^{2}}$$

Simplify

The graph

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Identical expressions

Derivative of x^2/log(x)

The graph:

Piecewise:

The solution