Derivative of x^x-1

The solution

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 x    
x  - 1

$$x^{x} - 1$$

x^x - 1

Detail solution

Differentiate $x^{x} - 1$ term by term:
1. Don't know the steps in finding this derivative.
  
  But the derivative is
  
  $x^{x} \left(\log{\left(x \right)} + 1\right)$
2. The derivative of the constant $-1$ is zero.
The result is: $x^{x} \left(\log{\left(x \right)} + 1\right)$

The answer is:

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

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 /1               2\
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 /            3   1    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

The graph

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Derivative of x^x-1

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The solution