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 x+5
-
Derivative of e^sinx
-
Derivative of x^2/(x+1)
-
Derivative of x^1/5
-
Identical expressions
- ((x^ two)+ one)/(|x|)
- ((x squared ) plus 1) divide by ( module of x|)
- ((x to the power of two) plus one) divide by ( module of x|)
- ((x2)+1)/(|x|)
- x2+1/|x|
- ((x²)+1)/(|x|)
- ((x to the power of 2)+1)/(|x|)
- x^2+1/|x|
- ((x^2)+1) divide by (|x|)
-
Similar expressions
- ((x^2)-1)/(|x|)
Derivative of ((x^2)+1)/(|x|)
The solution
The first derivative
[src]
/ 2 \
2*x \x + 1/*sign(x)
--- - ----------------
|x| 2
x
$$\frac{2 x}{\left|{x}\right|} - \frac{\left(x^{2} + 1\right) \operatorname{sign}{\left(x \right)}}{x^{2}}$$
The second derivative
[src]
/ / 2\ / sign(x) \\ | \1 + x /*|- ------- + DiracDelta(x)|| | 1 2*sign(x) \ x /| 2*|--- - --------- - ------------------------------------| ||x| x 2 | \ x /
$$2 \left(\frac{1}{\left|{x}\right|} - \frac{2 \operatorname{sign}{\left(x \right)}}{x} - \frac{\left(x^{2} + 1\right) \left(\delta\left(x\right) - \frac{\operatorname{sign}{\left(x \right)}}{x}\right)}{x^{2}}\right)$$
The third derivative
[src]
/ / 2\ / 4*DiracDelta(x) 3*sign(x) \\
| \1 + x /*|- --------------- + --------- + DiracDelta(x, 1)||
| | x 2 ||
| 3*sign(x) \ x /|
-2*|6*DiracDelta(x) - --------- + -----------------------------------------------------------|
\ x x /
----------------------------------------------------------------------------------------------
x
$$- \frac{2 \left(6 \delta\left(x\right) + \frac{\left(x^{2} + 1\right) \left(\delta^{\left( 1 \right)}\left( x \right) - \frac{4 \delta\left(x\right)}{x} + \frac{3 \operatorname{sign}{\left(x \right)}}{x^{2}}\right)}{x} - \frac{3 \operatorname{sign}{\left(x \right)}}{x}\right)}{x}$$