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
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How to use it?
- Derivative of:
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Derivative of e^-1
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Derivative of 2*x^5
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Derivative of sin(2*x^2+3)
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Derivative of f(x)=5
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Identical expressions
- |x|/(x^ two + one)
- module of x| divide by (x squared plus 1)
- module of x| divide by (x to the power of two plus one)
- |x|/(x2+1)
- |x|/x2+1
- |x|/(x²+1)
- |x|/(x to the power of 2+1)
- |x|/x^2+1
- |x| divide by (x^2+1)
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Similar expressions
- |x|/(x^2-1)
Derivative of |x|/(x^2+1)
The solution
The first derivative
[src]
sign(x) 2*x*|x|
------- - ---------
2 2
x + 1 / 2 \
\x + 1/
$$- \frac{2 x \left|{x}\right|}{\left(x^{2} + 1\right)^{2}} + \frac{\operatorname{sign}{\left(x \right)}}{x^{2} + 1}$$
The second derivative
[src]
// 2 \ \
|| 4*x | |
||-1 + ------|*|x| |
|| 2| |
|\ 1 + x / 2*x*sign(x) |
2*|----------------- - ----------- + DiracDelta(x)|
| 2 2 |
\ 1 + x 1 + x /
---------------------------------------------------
2
1 + x
$$\frac{2 \left(- \frac{2 x \operatorname{sign}{\left(x \right)}}{x^{2} + 1} + \delta\left(x\right) + \frac{\left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \left|{x}\right|}{x^{2} + 1}\right)}{x^{2} + 1}$$
The third derivative
[src]
/ / 2 \ / 2 \ \
| | 4*x | | 2*x | |
| 3*|-1 + ------|*sign(x) 12*x*|-1 + ------|*|x| |
| | 2| | 2| |
| 6*x*DiracDelta(x) \ 1 + x / \ 1 + x / |
2*|- ----------------- + ----------------------- - ---------------------- + DiracDelta(x, 1)|
| 2 2 2 |
| 1 + x 1 + x / 2\ |
\ \1 + x / /
---------------------------------------------------------------------------------------------
2
1 + x
$$\frac{2 \left(- \frac{6 x \delta\left(x\right)}{x^{2} + 1} - \frac{12 x \left(\frac{2 x^{2}}{x^{2} + 1} - 1\right) \left|{x}\right|}{\left(x^{2} + 1\right)^{2}} + \delta^{\left( 1 \right)}\left( x \right) + \frac{3 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \operatorname{sign}{\left(x \right)}}{x^{2} + 1}\right)}{x^{2} + 1}$$