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The derivative of the function/ e^x^x

Derivative of e^x^x

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 / x\
 \x /
E
$$e^{x^{x}}$$ 
E^(x^x)
Detail solution

  1. Let .

  2. The derivative of is itself.

  3. Then, apply the chain rule. Multiply by :

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

      But the derivative is

    The result of the chain rule is:

The answer is:

The first derivative [src] 
                 / x\
 x               \x /
x *(1 + log(x))*e
$$x^{x} \left(\log{\left(x \right)} + 1\right) e^{x^{x}}$$
Simplify
The second derivative [src] 
                                           / x\
 x /1               2    x             2\  \x /
x *|- + (1 + log(x))  + x *(1 + log(x)) |*e    
   \x                                   /
$$x^{x} \left(x^{x} \left(\log{\left(x \right)} + 1\right)^{2} + \left(\log{\left(x \right)} + 1\right)^{2} + \frac{1}{x}\right) e^{x^{x}}$$
Simplify
The third derivative [src] 
   /                                                                                   x             \  / x\
 x |            3   1     2*x             3   3*(1 + log(x))      x             3   3*x *(1 + log(x))|  \x /
x *|(1 + log(x))  - -- + x   *(1 + log(x))  + -------------- + 3*x *(1 + log(x))  + -----------------|*e    
   |                 2                              x                                       x        |      
   \                x                                                                                /
$$x^{x} \left(x^{2 x} \left(\log{\left(x \right)} + 1\right)^{3} + 3 x^{x} \left(\log{\left(x \right)} + 1\right)^{3} + \left(\log{\left(x \right)} + 1\right)^{3} + \frac{3 x^{x} \left(\log{\left(x \right)} + 1\right)}{x} + \frac{3 \left(\log{\left(x \right)} + 1\right)}{x} - \frac{1}{x^{2}}\right) e^{x^{x}}$$
Simplify
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