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

Derivative of exp(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 /
(ex)x\left(e^{x}\right)^{x} 
  /    x\
d |/ x\ |
--\\e / /
dx
ddx(ex)x\frac{d}{d x} \left(e^{x}\right)^{x}
Transform
Detail solution

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

    But the derivative is

    xx(log⁡(x)+1)x^{x} \left(\log{\left(x \right)} + 1\right)

The answer is:

xx(log⁡(x)+1)x^{x} \left(\log{\left(x \right)} + 1\right)

The graph
02468-8-6-4-2-10101e45-5e44
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     / 2\
     \x /
2*x*e
2xex22 x e^{x^{2}}
Simplify
The second derivative [src] 
              / 2\
  /       2\  \x /
2*\1 + 2*x /*e
2⋅(2x2+1)ex22 \cdot \left(2 x^{2} + 1\right) e^{x^{2}}
Simplify
The third derivative [src] 
                / 2\
    /       2\  \x /
4*x*\3 + 2*x /*e
4x(2x2+3)ex24 x \left(2 x^{2} + 3\right) e^{x^{2}}
Simplify
The graph
Derivative of exp(x)^x
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