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x^ln(x)
The derivative of the function/ x^ln(x)

Derivative of x^ln(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 log(x)
x
xlog⁡(x)x^{\log{\left(x \right)}} 
x^log(x)
Detail solution

  1. Don't know the steps in finding this derivative.

    But the derivative is

    (log⁡(log⁡(x))+1)log⁡(x)log⁡(x)\left(\log{\left(\log{\left(x \right)} \right)} + 1\right) \log{\left(x \right)}^{\log{\left(x \right)}}

The answer is:

(log⁡(log⁡(x))+1)log⁡(x)log⁡(x)\left(\log{\left(\log{\left(x \right)} \right)} + 1\right) \log{\left(x \right)}^{\log{\left(x \right)}}

The graph
02468-8-6-4-2-1010-1000010000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   log(x)       
2*x      *log(x)
----------------
       x
2xlog⁡(x)log⁡(x)x\frac{2 x^{\log{\left(x \right)}} \log{\left(x \right)}}{x}
Simplify
The second derivative [src] 
   log(x) /                  2   \
2*x      *\1 - log(x) + 2*log (x)/
----------------------------------
                 2                
                x
2xlog⁡(x)(2log⁡(x)2−log⁡(x)+1)x2\frac{2 x^{\log{\left(x \right)}} \left(2 \log{\left(x \right)}^{2} - \log{\left(x \right)} + 1\right)}{x^{2}}
Simplify
The third derivative [src] 
   log(x) /          2           3              \
2*x      *\-3 - 6*log (x) + 4*log (x) + 8*log(x)/
-------------------------------------------------
                         3                       
                        x
2xlog⁡(x)(4log⁡(x)3−6log⁡(x)2+8log⁡(x)−3)x3\frac{2 x^{\log{\left(x \right)}} \left(4 \log{\left(x \right)}^{3} - 6 \log{\left(x \right)}^{2} + 8 \log{\left(x \right)} - 3\right)}{x^{3}}
Simplify
The graph
Derivative of x^ln(x)
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