Mister Exam

Derivative of y^(y/2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
 y
 -
 2
y 
$$y^{\frac{y}{2}}$$
y^(y/2)
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]
 y             
 -             
 2 /1   log(y)\
y *|- + ------|
   \2     2   /
$$y^{\frac{y}{2}} \left(\frac{\log{\left(y \right)}}{2} + \frac{1}{2}\right)$$
The second derivative [src]
 y                    
 -                    
 2 /            2   2\
y *|(1 + log(y))  + -|
   \                y/
----------------------
          4           
$$\frac{y^{\frac{y}{2}} \left(\left(\log{\left(y \right)} + 1\right)^{2} + \frac{2}{y}\right)}{4}$$
The third derivative [src]
 y                                      
 -                                      
 2 /            3   4    6*(1 + log(y))\
y *|(1 + log(y))  - -- + --------------|
   |                 2         y       |
   \                y                  /
----------------------------------------
                   8                    
$$\frac{y^{\frac{y}{2}} \left(\left(\log{\left(y \right)} + 1\right)^{3} + \frac{6 \left(\log{\left(y \right)} + 1\right)}{y} - \frac{4}{y^{2}}\right)}{8}$$
The graph
Derivative of y^(y/2)