Derivative of y^(y/2)

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 y
 -
 2
y

$$y^{\frac{y}{2}}$$

y^(y/2)

Detail solution

Don't know the steps in finding this derivative.

But the derivative is

$\left(\frac{y}{2}\right)^{\frac{y}{2}} \left(\log{\left(\frac{y}{2} \right)} + 1\right)$
Now simplify:

$y^{\frac{y}{2}} \left(\frac{\sqrt{2}}{2}\right)^{y} \left(\log{\left(\frac{y}{2} \right)} + 1\right)$

The answer is:

$y^{\frac{y}{2}} \left(\frac{\sqrt{2}}{2}\right)^{y} \left(\log{\left(\frac{y}{2} \right)} + 1\right)$

The graph

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The first derivative [src]

 y             
 -             
 2 /1   log(y)\
y *|- + ------|
   \2     2   /

$$y^{\frac{y}{2}} \left(\frac{\log{\left(y \right)}}{2} + \frac{1}{2}\right)$$

Simplify

The second derivative [src]

 y                    
 -                    
 2 /            2   2\
y *|(1 + log(y))  + -|
   \                y/
----------------------
          4

$$\frac{y^{\frac{y}{2}} \left(\left(\log{\left(y \right)} + 1\right)^{2} + \frac{2}{y}\right)}{4}$$

Simplify

The third derivative [src]

 y                                      
 -                                      
 2 /            3   4    6*(1 + log(y))\
y *|(1 + log(y))  - -- + --------------|
   |                 2         y       |
   \                y                  /
----------------------------------------
                   8

$$\frac{y^{\frac{y}{2}} \left(\left(\log{\left(y \right)} + 1\right)^{3} + \frac{6 \left(\log{\left(y \right)} + 1\right)}{y} - \frac{4}{y^{2}}\right)}{8}$$

Simplify

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Identical expressions

Derivative of y^(y/2)

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Piecewise:

The solution