Mister Exam

Derivative of |x|/x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
|x|
---
 x 
$$\frac{\left|{x}\right|}{x}$$
|x|/x
The first derivative [src]
sign(x)   |x|
------- - ---
   x        2
           x 
$$\frac{\operatorname{sign}{\left(x \right)}}{x} - \frac{\left|{x}\right|}{x^{2}}$$
The second derivative [src]
  /|x|   sign(x)                \
2*|--- - ------- + DiracDelta(x)|
  |  2      x                   |
  \ x                           /
---------------------------------
                x                
$$\frac{2 \left(\delta\left(x\right) - \frac{\operatorname{sign}{\left(x \right)}}{x} + \frac{\left|{x}\right|}{x^{2}}\right)}{x}$$
The third derivative [src]
  /  3*DiracDelta(x)   3*|x|   3*sign(x)                   \
2*|- --------------- - ----- + --------- + DiracDelta(x, 1)|
  |         x             3         2                      |
  \                      x         x                       /
------------------------------------------------------------
                             x                              
$$\frac{2 \left(\delta^{\left( 1 \right)}\left( x \right) - \frac{3 \delta\left(x\right)}{x} + \frac{3 \operatorname{sign}{\left(x \right)}}{x^{2}} - \frac{3 \left|{x}\right|}{x^{3}}\right)}{x}$$