Mister Exam
Other calculators
- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Derivative of:
-
Derivative of 2*cos(3*x)
-
Derivative of 1^3*sqrt(x)
-
Derivative of (x+4)/(x-1)
-
Derivative of (x-3)^4
- Graphing y =:
- |x|/x
- Integral of d{x}:
- |x|/x
- Limit of the function:
-
|x|/x
-
Identical expressions
- |x|/x
- module of x| divide by x
- |x| divide by x
-
Similar expressions
- y=ln(|x|)/x
- |x|/(x^2+1)
Derivative of |x|/x
The solution
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
$$\frac{2 \left(\delta^{\left( 1 \right)}\left( x \right) - \frac{3 \delta\left(x\right)}{x} + \frac{3 \operatorname{sign}{\left(x \right)}}{x^{2}} - \frac{3 \left|{x}\right|}{x^{3}}\right)}{x}$$