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

Derivative of y^ln(y)

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

The graph:

from to

Piecewise:

The solution

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

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

    But the derivative is

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

The answer is:

(log⁡(log⁡(y))+1)log⁡(y)log⁡(y)\left(\log{\left(\log{\left(y \right)} \right)} + 1\right) \log{\left(y \right)}^{\log{\left(y \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(y)       
2*y      *log(y)
----------------
       y
2ylog⁡(y)log⁡(y)y\frac{2 y^{\log{\left(y \right)}} \log{\left(y \right)}}{y}
Simplify
The second derivative [src] 
   log(y) /                  2   \
2*y      *\1 - log(y) + 2*log (y)/
----------------------------------
                 2                
                y
2ylog⁡(y)(2log⁡(y)2−log⁡(y)+1)y2\frac{2 y^{\log{\left(y \right)}} \left(2 \log{\left(y \right)}^{2} - \log{\left(y \right)} + 1\right)}{y^{2}}
Simplify
The third derivative [src] 
   log(y) /          2           3              \
2*y      *\-3 - 6*log (y) + 4*log (y) + 8*log(y)/
-------------------------------------------------
                         3                       
                        y
2ylog⁡(y)(4log⁡(y)3−6log⁡(y)2+8log⁡(y)−3)y3\frac{2 y^{\log{\left(y \right)}} \left(4 \log{\left(y \right)}^{3} - 6 \log{\left(y \right)}^{2} + 8 \log{\left(y \right)} - 3\right)}{y^{3}}
Simplify
The graph
Derivative of y^ln(y)
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