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Derivada de la función/ y=sqrt(x^3+x)/sqrt((x-1)^2)

Derivada de y=sqrt(x^3+x)/sqrt((x-1)^2)

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

Gráfico:

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Solución

Ha introducido [src] 
    ________ 
   /  3      
 \/  x  + x  
-------------
   __________
  /        2 
\/  (x - 1)
x3+x(x−1)2\frac{\sqrt{x^{3} + x}}{\sqrt{\left(x - 1\right)^{2}}} 
sqrt(x^3 + x)/sqrt((x - 1)^2)
Gráfica
02468-8-6-4-2-1010-500500
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Trazar el gráfico f'(x)
Primera derivada [src] 
             2                            
      1   3*x            ________         
      - + ----          /  3              
      2    2          \/  x  + x *(-1 + x)
------------------- - --------------------
   ________                    2          
  /  3                  (x - 1) *|x - 1|  
\/  x  + x *|x - 1|
−(x−1)x3+x(x−1)2∣x−1∣+3x22+12x3+x∣x−1∣- \frac{\left(x - 1\right) \sqrt{x^{3} + x}}{\left(x - 1\right)^{2} \left|{x - 1}\right|} + \frac{\frac{3 x^{2}}{2} + \frac{1}{2}}{\sqrt{x^{3} + x} \left|{x - 1}\right|}
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Segunda derivada [src] 
                      2                                                                                     
            /       2\                                                                                      
     ___    \1 + 3*x /              ________                                                                
12*\/ x  - -------------     ___   /      2  /   1       sign(-1 + x)\                                      
            3/2 /     2\   \/ x *\/  1 + x  *|-------- + ------------|                        2             
           x   *\1 + x /                     \|-1 + x|      -1 + x   /                 1 + 3*x              
------------------------ + ------------------------------------------- - -----------------------------------
      ________                                      2                             ________                  
     /      2                               (-1 + x)                       ___   /      2                   
 4*\/  1 + x  *|-1 + x|                                                  \/ x *\/  1 + x  *(-1 + x)*|-1 + x|
xx2+1(1∣x−1∣+sign⁡(x−1)x−1)(x−1)2+12x−(3x2+1)2x32(x2+1)4x2+1∣x−1∣−3x2+1x(x−1)x2+1∣x−1∣\frac{\sqrt{x} \sqrt{x^{2} + 1} \left(\frac{1}{\left|{x - 1}\right|} + \frac{\operatorname{sign}{\left(x - 1 \right)}}{x - 1}\right)}{\left(x - 1\right)^{2}} + \frac{12 \sqrt{x} - \frac{\left(3 x^{2} + 1\right)^{2}}{x^{\frac{3}{2}} \left(x^{2} + 1\right)}}{4 \sqrt{x^{2} + 1} \left|{x - 1}\right|} - \frac{3 x^{2} + 1}{\sqrt{x} \left(x - 1\right) \sqrt{x^{2} + 1} \left|{x - 1}\right|}
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Tercera derivada [src] 
                                                                                                             /                              3 \                                         
                                                                             /                      2 \      |       /       2\   /       2\  |                                         
                                                                             |            /       2\  |      |    12*\1 + 3*x /   \1 + 3*x /  |                                         
             ________                                                        |     ___    \1 + 3*x /  |    3*|8 - ------------- + ------------|                                         
      ___   /      2  /   1                            2*sign(-1 + x)\     3*|12*\/ x  - -------------|      |             2                 2|     /       2\ /   1       sign(-1 + x)\
  2*\/ x *\/  1 + x  *|-------- - DiracDelta(-1 + x) + --------------|       |            3/2 /     2\|      |        1 + x        2 /     2\ |   3*\1 + 3*x /*|-------- + ------------|
                      \|-1 + x|                            -1 + x    /       \           x   *\1 + x //      \                    x *\1 + x / /                \|-1 + x|      -1 + x   /
- -------------------------------------------------------------------- - ------------------------------- + ------------------------------------ + --------------------------------------
                                       3                                      ________                                    ________                               ________               
                               (-1 + x)                                      /      2                              ___   /      2                         ___   /      2          2     
                                                                         4*\/  1 + x  *(-1 + x)*|-1 + x|       8*\/ x *\/  1 + x  *|-1 + x|           2*\/ x *\/  1 + x  *(-1 + x)
−2xx2+1(−δ(x−1)+1∣x−1∣+2sign⁡(x−1)x−1)(x−1)3−3(12x−(3x2+1)2x32(x2+1))4(x−1)x2+1∣x−1∣+3(8−12(3x2+1)x2+1+(3x2+1)3x2(x2+1)2)8xx2+1∣x−1∣+3(3x2+1)(1∣x−1∣+sign⁡(x−1)x−1)2x(x−1)2x2+1- \frac{2 \sqrt{x} \sqrt{x^{2} + 1} \left(- \delta\left(x - 1\right) + \frac{1}{\left|{x - 1}\right|} + \frac{2 \operatorname{sign}{\left(x - 1 \right)}}{x - 1}\right)}{\left(x - 1\right)^{3}} - \frac{3 \left(12 \sqrt{x} - \frac{\left(3 x^{2} + 1\right)^{2}}{x^{\frac{3}{2}} \left(x^{2} + 1\right)}\right)}{4 \left(x - 1\right) \sqrt{x^{2} + 1} \left|{x - 1}\right|} + \frac{3 \left(8 - \frac{12 \left(3 x^{2} + 1\right)}{x^{2} + 1} + \frac{\left(3 x^{2} + 1\right)^{3}}{x^{2} \left(x^{2} + 1\right)^{2}}\right)}{8 \sqrt{x} \sqrt{x^{2} + 1} \left|{x - 1}\right|} + \frac{3 \left(3 x^{2} + 1\right) \left(\frac{1}{\left|{x - 1}\right|} + \frac{\operatorname{sign}{\left(x - 1 \right)}}{x - 1}\right)}{2 \sqrt{x} \left(x - 1\right)^{2} \sqrt{x^{2} + 1}}
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