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Derivada de la función/ (x^2)/ x/(sqrt(x^2)+1)

Derivada de x/(sqrt(x^2)+1)

Función f() - derivada -er orden en el punto
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
     x     
-----------
   ____    
  /  2     
\/  x   + 1
xx2+1\frac{x}{\sqrt{x^{2}} + 1} 
x/(sqrt(x^2) + 1)
Primera derivada [src] 
     1             |x|      
----------- - --------------
   ____                    2
  /  2        /   ____    \ 
\/  x   + 1   |  /  2     | 
              \\/  x   + 1/
1x2+1−∣x∣(x2+1)2\frac{1}{\sqrt{x^{2}} + 1} - \frac{\left|{x}\right|}{\left(\sqrt{x^{2}} + 1\right)^{2}}
Simplificar
Segunda derivada [src] 
  /   2      |x|   sign(x)\   2*|x|
x*|------- + --- - -------| - -----
  |1 + |x|     2      x   |     x  
  \           x           /        
-----------------------------------
                      2            
             (1 + |x|)
x(2∣x∣+1−sign⁡(x)x+∣x∣x2)−2∣x∣x(∣x∣+1)2\frac{x \left(\frac{2}{\left|{x}\right| + 1} - \frac{\operatorname{sign}{\left(x \right)}}{x} + \frac{\left|{x}\right|}{x^{2}}\right) - \frac{2 \left|{x}\right|}{x}}{\left(\left|{x}\right| + 1\right)^{2}}
Simplificar
Tercera derivada [src] 
                      4      |x|   sign(x)     6*|x|      2*|x|*sign(x)
-2*DiracDelta(x) + ------- + --- - ------- - ---------- + -------------
                   1 + |x|     2      x               2    x*(1 + |x|) 
                              x              (1 + |x|)                 
-----------------------------------------------------------------------
                                        2                              
                               (1 + |x|)
−2δ(x)+4∣x∣+1−6∣x∣(∣x∣+1)2−sign⁡(x)x+2∣x∣sign⁡(x)x(∣x∣+1)+∣x∣x2(∣x∣+1)2\frac{- 2 \delta\left(x\right) + \frac{4}{\left|{x}\right| + 1} - \frac{6 \left|{x}\right|}{\left(\left|{x}\right| + 1\right)^{2}} - \frac{\operatorname{sign}{\left(x \right)}}{x} + \frac{2 \left|{x}\right| \operatorname{sign}{\left(x \right)}}{x \left(\left|{x}\right| + 1\right)} + \frac{\left|{x}\right|}{x^{2}}}{\left(\left|{x}\right| + 1\right)^{2}}
Simplificar
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