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Derivative of x^(2ln(x)/x(3))

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
 2*log(x)  
 --------*3
    x      
x          
$$x^{3 \frac{2 \log{\left(x \right)}}{x}}$$
x^(((2*log(x))/x)*3)
Detail solution
  1. Don't know the steps in finding this derivative.

    But the derivative is

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
 2*log(x)                                      
 --------*3                                    
    x       //6    6*log(x)\          6*log(x)\
x          *||-- - --------|*log(x) + --------|
            || 2       2   |              2   |
            \\x       x    /             x    /
$$x^{3 \frac{2 \log{\left(x \right)}}{x}} \left(\left(- \frac{6 \log{\left(x \right)}}{x^{2}} + \frac{6}{x^{2}}\right) \log{\left(x \right)} + \frac{6 \log{\left(x \right)}}{x^{2}}\right)$$
The second derivative [src]
   6*log(x)                                                                   
   -------- /                                                       2    2   \
      x     |                                        6*(-2 + log(x)) *log (x)|
6*x        *|2 - 3*log(x) + (-3 + 2*log(x))*log(x) + ------------------------|
            \                                                   x            /
------------------------------------------------------------------------------
                                       3                                      
                                      x                                       
$$\frac{6 x^{\frac{6 \log{\left(x \right)}}{x}} \left(\left(2 \log{\left(x \right)} - 3\right) \log{\left(x \right)} - 3 \log{\left(x \right)} + 2 + \frac{6 \left(\log{\left(x \right)} - 2\right)^{2} \log{\left(x \right)}^{2}}{x}\right)}{x^{3}}$$
The third derivative [src]
   6*log(x)                                                                                                                                          
   -------- /                                                            3    3                                                                     \
      x     |                                            36*(-2 + log(x)) *log (x)   18*(-2 + log(x))*(2 - 3*log(x) + (-3 + 2*log(x))*log(x))*log(x)|
6*x        *|-12 + 11*log(x) - (-11 + 6*log(x))*log(x) - ------------------------- - ---------------------------------------------------------------|
            |                                                         2                                             x                               |
            \                                                        x                                                                              /
-----------------------------------------------------------------------------------------------------------------------------------------------------
                                                                           4                                                                         
                                                                          x                                                                          
$$\frac{6 x^{\frac{6 \log{\left(x \right)}}{x}} \left(- \left(6 \log{\left(x \right)} - 11\right) \log{\left(x \right)} + 11 \log{\left(x \right)} - 12 - \frac{18 \left(\log{\left(x \right)} - 2\right) \left(\left(2 \log{\left(x \right)} - 3\right) \log{\left(x \right)} - 3 \log{\left(x \right)} + 2\right) \log{\left(x \right)}}{x} - \frac{36 \left(\log{\left(x \right)} - 2\right)^{3} \log{\left(x \right)}^{3}}{x^{2}}\right)}{x^{4}}$$