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x^(x+1)
The derivative of the function/ x^(x+1)

Derivative of x^(x+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 x + 1
x
$$x^{x + 1}$$ 
x^(x + 1)
Detail solution

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

    But the derivative is

  2. Now simplify:

The answer is:

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