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

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

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

Gráfico:

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Solución

Ha introducido [src] 
     _______   
   \/ x - 1    
---------------
   ____        
  /  2         
\/  x   - x - 1
x−1(−x+x2)−1\frac{\sqrt{x - 1}}{\left(- x + \sqrt{x^{2}}\right) - 1} 
sqrt(x - 1)/(sqrt(x^2) - x - 1)
Primera derivada [src] 
                                  _______ /    |x|\
                                \/ x - 1 *|1 - ---|
              1                           \     x /
----------------------------- + -------------------
            /   ____        \                     2
    _______ |  /  2         |    /   ____        \ 
2*\/ x - 1 *\\/  x   - x - 1/    |  /  2         | 
                                 \\/  x   - x - 1/
(1−∣x∣x)x−1((−x+x2)−1)2+12x−1((−x+x2)−1)\frac{\left(1 - \frac{\left|{x}\right|}{x}\right) \sqrt{x - 1}}{\left(\left(- x + \sqrt{x^{2}}\right) - 1\right)^{2}} + \frac{1}{2 \sqrt{x - 1} \left(\left(- x + \sqrt{x^{2}}\right) - 1\right)}
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Segunda derivada [src] 
                                                      /                             2\
                                                      |  |x|               /    |x|\ |
                                                      |- --- + sign(x)   2*|1 - ---| |
                            |x|              ________ |   x                \     x / |
                        1 - ---            \/ -1 + x *|--------------- + ------------|
      1                      x                        \       x          1 + x - |x| /
------------- + ------------------------ - -------------------------------------------
          3/2     ________                                 1 + x - |x|                
4*(-1 + x)      \/ -1 + x *(1 + x - |x|)                                              
--------------------------------------------------------------------------------------
                                     1 + x - |x|
1−∣x∣xx−1(x−∣x∣+1)−x−1(2(1−∣x∣x)2x−∣x∣+1+sign⁡(x)−∣x∣xx)x−∣x∣+1+14(x−1)32x−∣x∣+1\frac{\frac{1 - \frac{\left|{x}\right|}{x}}{\sqrt{x - 1} \left(x - \left|{x}\right| + 1\right)} - \frac{\sqrt{x - 1} \left(\frac{2 \left(1 - \frac{\left|{x}\right|}{x}\right)^{2}}{x - \left|{x}\right| + 1} + \frac{\operatorname{sign}{\left(x \right)} - \frac{\left|{x}\right|}{x}}{x}\right)}{x - \left|{x}\right| + 1} + \frac{1}{4 \left(x - 1\right)^{\frac{3}{2}}}}{x - \left|{x}\right| + 1}
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Tercera derivada [src] 
                               /  |x|   sign(x)                               3                                 \                                                                   
                               |  --- - ------- + DiracDelta(x)      /    |x|\       /    |x|\ /  |x|          \|     /                             2\                              
                               |    2      x                       3*|1 - ---|     3*|1 - ---|*|- --- + sign(x)||     |  |x|               /    |x|\ |                              
                      ________ |   x                                 \     x /       \     x / \   x           /|     |- --- + sign(x)   2*|1 - ---| |                              
                  2*\/ -1 + x *|- ----------------------------- + -------------- + -----------------------------|     |   x                \     x / |             /    |x|\        
                               |                x                              2          x*(1 + x - |x|)       |   3*|--------------- + ------------|           3*|1 - ---|        
        3                      \                                  (1 + x - |x|)                                 /     \       x          1 + x - |x| /             \     x /        
- ------------- + ----------------------------------------------------------------------------------------------- - ---------------------------------- - ---------------------------
            5/2                                             1 + x - |x|                                                     ________                               3/2              
  8*(-1 + x)                                                                                                            2*\/ -1 + x *(1 + x - |x|)       4*(-1 + x)   *(1 + x - |x|)
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                    1 + x - |x|
−3(1−∣x∣x)4(x−1)32(x−∣x∣+1)+2x−1(3(1−∣x∣x)3(x−∣x∣+1)2+3(1−∣x∣x)(sign⁡(x)−∣x∣x)x(x−∣x∣+1)−δ(x)−sign⁡(x)x+∣x∣x2x)x−∣x∣+1−3(2(1−∣x∣x)2x−∣x∣+1+sign⁡(x)−∣x∣xx)2x−1(x−∣x∣+1)−38(x−1)52x−∣x∣+1\frac{- \frac{3 \left(1 - \frac{\left|{x}\right|}{x}\right)}{4 \left(x - 1\right)^{\frac{3}{2}} \left(x - \left|{x}\right| + 1\right)} + \frac{2 \sqrt{x - 1} \left(\frac{3 \left(1 - \frac{\left|{x}\right|}{x}\right)^{3}}{\left(x - \left|{x}\right| + 1\right)^{2}} + \frac{3 \left(1 - \frac{\left|{x}\right|}{x}\right) \left(\operatorname{sign}{\left(x \right)} - \frac{\left|{x}\right|}{x}\right)}{x \left(x - \left|{x}\right| + 1\right)} - \frac{\delta\left(x\right) - \frac{\operatorname{sign}{\left(x \right)}}{x} + \frac{\left|{x}\right|}{x^{2}}}{x}\right)}{x - \left|{x}\right| + 1} - \frac{3 \left(\frac{2 \left(1 - \frac{\left|{x}\right|}{x}\right)^{2}}{x - \left|{x}\right| + 1} + \frac{\operatorname{sign}{\left(x \right)} - \frac{\left|{x}\right|}{x}}{x}\right)}{2 \sqrt{x - 1} \left(x - \left|{x}\right| + 1\right)} - \frac{3}{8 \left(x - 1\right)^{\frac{5}{2}}}}{x - \left|{x}\right| + 1}
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