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

Derivative of (1/x)^x

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

The graph:

from to

Piecewise:

The solution

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