Derivative of y^y

The solution

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y
y

$$y^{y}$$

y^y

Detail solution

Don't know the steps in finding this derivative.

But the derivative is

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

The answer is:

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

The graph

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The first derivative [src]

 y             
y *(1 + log(y))

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify

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Identical expressions

Derivative of y^y

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The solution