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The derivative of the function/ x^(-x)

Derivative of x^(-x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 -x
x
$$x^{- x}$$ 
x^(-x)
Detail solution

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

    But the derivative is

The answer is:

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