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xex
The derivative of the function/ xex

Derivative of xex

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 / x\
 \e /
x
$$x^{e^{x}}$$ 
  / / x\\
d | \e /|
--\x    /
dx
$$\frac{d}{d x} x^{e^{x}}$$
Transform
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            \
 \e / |e     x       |
x    *|-- + e *log(x)|
      \x             /
$$x^{e^{x}} \left(e^{x} \log{\left(x \right)} + \frac{e^{x}}{x}\right)$$
Simplify
The second derivative [src] 
 / x\ /                       2            \   
 \e / |  1    2   /1         \   x         |  x
x    *|- -- + - + |- + log(x)| *e  + log(x)|*e 
      |   2   x   \x         /             |   
      \  x                                 /
$$x^{e^{x}} \left(\left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{x} + \log{\left(x \right)} + \frac{2}{x} - \frac{1}{x^{2}}\right) e^{x}$$
Simplify
The third derivative [src] 
 / x\ /                            3                                                      \   
 \e / |  3    2    3   /1         \   2*x     /1         \ /  1    2         \  x         |  x
x    *|- -- + -- + - + |- + log(x)| *e    + 3*|- + log(x)|*|- -- + - + log(x)|*e  + log(x)|*e 
      |   2    3   x   \x         /           \x         / |   2   x         |            |   
      \  x    x                                            \  x              /            /
$$x^{e^{x}} \left(\left(\log{\left(x \right)} + \frac{1}{x}\right)^{3} e^{2 x} + 3 \left(\log{\left(x \right)} + \frac{1}{x}\right) \left(\log{\left(x \right)} + \frac{2}{x} - \frac{1}{x^{2}}\right) e^{x} + \log{\left(x \right)} + \frac{3}{x} - \frac{3}{x^{2}} + \frac{2}{x^{3}}\right) e^{x}$$
Simplify
The graph
Derivative of xex
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