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Expresiones semejantes
((x*(x+1)^3)/(((x+1)^5)*(x-2)))^1/2
((x*(x-1)^3)/(((x+1)^5)*(x+2)))^1/2
((x*(x-1)^3)/(((x-1)^5)*(x-2)))^1/2

Derivada de la función/ ((x*(x-1)^3)/(((x+1)^5)*(x-2)))^1/2

Derivada de ((x(x-1)^3)/(((x+1)^5)(x-2)))^1/2

Solución

Ha introducido [src]

      __________________
     /             3    
    /     x*(x - 1)     
   /   ---------------- 
  /           5         
\/     (x + 1) *(x - 2)

$$\sqrt{\frac{x \left(x - 1\right)^{3}}{\left(x - 2\right) \left(x + 1\right)^{5}}}$$

sqrt((x*(x - 1)^3)/(((x + 1)^5*(x - 2))))

Solución detallada

Sustituimos $u = \frac{x \left(x - 1\right)^{3}}{\left(x - 2\right) \left(x + 1\right)^{5}}$ .
Según el principio, aplicamos: $\sqrt{u}$ tenemos $\frac{1}{2 \sqrt{u}}$
Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \frac{x \left(x - 1\right)^{3}}{\left(x - 2\right) \left(x + 1\right)^{5}}$ :
1. Se aplica la regla de la derivada parcial:
  
  $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
  
  $f{\left(x \right)} = x \left(x - 1\right)^{3}$ y $g{\left(x \right)} = \left(x - 2\right) \left(x + 1\right)^{5}$ .
  
  Para calcular $\frac{d}{d x} f{\left(x \right)}$ :
  1. Se aplica la regla de la derivada de una multiplicación:
    
    $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
    
    $f{\left(x \right)} = x$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
    1. Según el principio, aplicamos: $x$ tenemos $1$
    $g{\left(x \right)} = \left(x - 1\right)^{3}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
    1. Sustituimos $u = x - 1$ .
    2. Según el principio, aplicamos: $u^{3}$ tenemos $3 u^{2}$
    3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \left(x - 1\right)$ :
      1. diferenciamos $x - 1$ miembro por miembro:
        
        La derivada de una constante $-1$ es igual a cero.
        
        Según el principio, aplicamos: $x$ tenemos $1$
        
        Como resultado de: $1$
      Como resultado de la secuencia de reglas:
      
      $3 \left(x - 1\right)^{2}$
    Como resultado de: $3 x \left(x - 1\right)^{2} + \left(x - 1\right)^{3}$
  Para calcular $\frac{d}{d x} g{\left(x \right)}$ :
  1. Se aplica la regla de la derivada de una multiplicación:
    
    $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
    
    $f{\left(x \right)} = \left(x + 1\right)^{5}$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
    1. Sustituimos $u = x + 1$ .
    2. Según el principio, aplicamos: $u^{5}$ tenemos $5 u^{4}$
    3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \left(x + 1\right)$ :
      1. diferenciamos $x + 1$ miembro por miembro:
        
        La derivada de una constante $1$ es igual a cero.
        
        Según el principio, aplicamos: $x$ tenemos $1$
        
        Como resultado de: $1$
      Como resultado de la secuencia de reglas:
      
      $5 \left(x + 1\right)^{4}$
    $g{\left(x \right)} = x - 2$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
    1. diferenciamos $x - 2$ miembro por miembro:
      1. La derivada de una constante $-2$ es igual a cero.
      2. Según el principio, aplicamos: $x$ tenemos $1$
      Como resultado de: $1$
    Como resultado de: $5 \left(x - 2\right) \left(x + 1\right)^{4} + \left(x + 1\right)^{5}$
  Ahora aplicamos la regla de la derivada de una divesión:
  
  $\frac{- x \left(x - 1\right)^{3} \left(5 \left(x - 2\right) \left(x + 1\right)^{4} + \left(x + 1\right)^{5}\right) + \left(x - 2\right) \left(x + 1\right)^{5} \left(3 x \left(x - 1\right)^{2} + \left(x - 1\right)^{3}\right)}{\left(x - 2\right)^{2} \left(x + 1\right)^{10}}$
Como resultado de la secuencia de reglas:

$\frac{- x \left(x - 1\right)^{3} \left(5 \left(x - 2\right) \left(x + 1\right)^{4} + \left(x + 1\right)^{5}\right) + \left(x - 2\right) \left(x + 1\right)^{5} \left(3 x \left(x - 1\right)^{2} + \left(x - 1\right)^{3}\right)}{2 \sqrt{\frac{x \left(x - 1\right)^{3}}{\left(x - 2\right) \left(x + 1\right)^{5}}} \left(x - 2\right)^{2} \left(x + 1\right)^{10}}$
Simplificamos:

$\frac{\left(x - 1\right)^{2} \left(- 3 x \left(x - 1\right) \left(2 x - 3\right) + \left(x - 2\right) \left(x + 1\right) \left(4 x - 1\right)\right)}{2 \sqrt{\frac{x \left(x - 1\right)^{3}}{\left(x - 2\right) \left(x + 1\right)^{5}}} \left(x - 2\right)^{2} \left(x + 1\right)^{6}}$

Respuesta:

$\frac{\left(x - 1\right)^{2} \left(- 3 x \left(x - 1\right) \left(2 x - 3\right) + \left(x - 2\right) \left(x + 1\right) \left(4 x - 1\right)\right)}{2 \sqrt{\frac{x \left(x - 1\right)^{3}}{\left(x - 2\right) \left(x + 1\right)^{5}}} \left(x - 2\right)^{2} \left(x + 1\right)^{6}}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

                                                    /       1         /       3              2\                                               \
                                                    |----------------*\(x - 1)  + 3*x*(x - 1) /                                               |
     _____________________________                  |       5                                              3 /         5            4        \|
    /          3        1                 5         |(x + 1) *(x - 2)                             x*(x - 1) *\- (x + 1)  - 5*(x + 1) *(x - 2)/|
   /  x*(x - 1) *---------------- *(x + 1) *(x - 2)*|------------------------------------------ + --------------------------------------------|
  /                     5                           |                    2                                             10        2            |
\/               (x + 1) *(x - 2)                   \                                                         2*(x + 1)  *(x - 2)             /
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                                                                            3                                                                  
                                                                   x*(x - 1)

$$\frac{\sqrt{x \frac{1}{\left(x - 2\right) \left(x + 1\right)^{5}} \left(x - 1\right)^{3}} \left(x - 2\right) \left(x + 1\right)^{5} \left(\frac{x \left(x - 1\right)^{3} \left(- 5 \left(x - 2\right) \left(x + 1\right)^{4} - \left(x + 1\right)^{5}\right)}{2 \left(x - 2\right)^{2} \left(x + 1\right)^{10}} + \frac{\frac{1}{\left(x - 2\right) \left(x + 1\right)^{5}} \left(3 x \left(x - 1\right)^{2} + \left(x - 1\right)^{3}\right)}{2}\right)}{x \left(x - 1\right)^{3}}$$

Simplificar

Segunda derivada [src]

                          /                                             /                                                            2                             3                 2                          2                                     \                                                                                                                                                                                                       \
                          |                                             |                               /  1        5  \   3*(-1 + x) *(-3 + 2*x)     30*x*(-1 + x)     30*x*(-1 + x) *(-3 + 2*x)   6*x*(-1 + x) *(-3 + 2*x)   9*x*(-1 + x)*(-3 + 2*x)|                                                                                                                                                                                                       |
      ___________________ |     /          3*x*(-1 + x)*(-3 + 2*x)\   2*|6 - 12*x + (-1 + x)*(-1 + 4*x)*|------ + -----| + ---------------------- + ----------------- - ------------------------- - ------------------------ + -----------------------|     /          3*x*(-1 + x)*(-3 + 2*x)\     /          3*x*(-1 + x)*(-3 + 2*x)\     /          3*x*(-1 + x)*(-3 + 2*x)\   /          3*x*(-1 + x)*(-3 + 2*x)\ /                      /  1        5  \\|
     /              3     |  10*|1 - 4*x + -----------------------|     |                               \-2 + x   1 + x/      (1 + x)*(-2 + x)             2                       2                                   2           (1 + x)*(-2 + x)   |   2*|1 - 4*x + -----------------------|   2*|1 - 4*x + -----------------------|   6*|1 - 4*x + -----------------------|   |1 - 4*x + -----------------------|*|-1 + 4*x - x*(-1 + x)*|------ + -----|||
    /     x*(-1 + x)      |     \              (1 + x)*(-2 + x)   /     \                                                                           (1 + x) *(-2 + x)       (1 + x) *(-2 + x)          (1 + x)*(-2 + x)                               /     \              (1 + x)*(-2 + x)   /     \              (1 + x)*(-2 + x)   /     \              (1 + x)*(-2 + x)   /   \              (1 + x)*(-2 + x)   / \                      \-2 + x   1 + x//|
   /   ----------------- *|- -------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------- + ------------------------------------- + ------------------------------------- - ----------------------------------------------------------------------------|
  /           5           \                  1 + x                                                                                                          -1 + x                                                                                                        -2 + x                                    x                                     -1 + x                                                   x*(-1 + x)                                 /
\/     (1 + x) *(-2 + x)                                                                                                                                                                                                                                                                                                                                                                                                                                       
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                          4*x*(-1 + x)

Simplificar

Tercera derivada [src]

                          /                                                                                                                                                                                                                          4                    4                   4                3                        3                        2                             3                 2                           2                          3                                                     3                           3                            3                                                                                                 /                                                            2                             3                 2                          2                                     \                                                               2                             3                 2                          2                                                                                                                                        2                             3                 2                          2                                          /                                                            2                             3                 2                          2                                     \                                                                                                                                                                                                                                                                                                                                                                                                                  /                                                            2                             3                 2                          2                                     \                                                                                                                   /                   2                                          2                                                                                                                         \                                         /                                                            2                             3                 2                          2                                     \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                \
                          |                                                         2            /    1          15             5        \   3*(-1 + x)*(-1 + 2*x)                         /  1        5  \   15*(-1 + x)*(-1 + 2*x)      30*(-1 + x)       300*x*(-1 + x)       60*x*(-1 + x)      30*(-1 + x) *(-3 + 2*x)   6*(-1 + x) *(-3 + 2*x)   9*(-1 + x) *(-3 + 2*x)     90*x*(-1 + x)     90*x*(-1 + x) *(-3 + 2*x)   18*x*(-1 + x) *(-3 + 2*x)   9*x*(-1 + x) *(-3 + 2*x)   9*x*(-1 + x)*(-3 + 2*x)   30*x*(-1 + x) *(-1 + 2*x)   60*x*(-1 + x) *(-3 + 2*x)   165*x*(-1 + x) *(-3 + 2*x)                                                                                      |                               /  1        5  \   3*(-1 + x) *(-3 + 2*x)     30*x*(-1 + x)     30*x*(-1 + x) *(-3 + 2*x)   6*x*(-1 + x) *(-3 + 2*x)   9*x*(-1 + x)*(-3 + 2*x)|                                  /  1        5  \   3*(-1 + x) *(-3 + 2*x)     30*x*(-1 + x)     30*x*(-1 + x) *(-3 + 2*x)   6*x*(-1 + x) *(-3 + 2*x)   9*x*(-1 + x)*(-3 + 2*x)                                                                      /  1        5  \   3*(-1 + x) *(-3 + 2*x)     30*x*(-1 + x)     30*x*(-1 + x) *(-3 + 2*x)   6*x*(-1 + x) *(-3 + 2*x)   9*x*(-1 + x)*(-3 + 2*x)     |                               /  1        5  \   3*(-1 + x) *(-3 + 2*x)     30*x*(-1 + x)     30*x*(-1 + x) *(-3 + 2*x)   6*x*(-1 + x) *(-3 + 2*x)   9*x*(-1 + x)*(-3 + 2*x)|                                                                                                                                                                                                                                                                                                                                                                         /                      /  1        5  \\ |                               /  1        5  \   3*(-1 + x) *(-3 + 2*x)     30*x*(-1 + x)     30*x*(-1 + x) *(-3 + 2*x)   6*x*(-1 + x) *(-3 + 2*x)   9*x*(-1 + x)*(-3 + 2*x)|                                                                               /          3*x*(-1 + x)*(-3 + 2*x)\ |           (-1 + x)            2 /  1        5  \   5*(-1 + x)                2 /    1          15             5        \   3*x*(-1 + x)                /  1        5  \   15*x*(-1 + x)|   /          x*(-1 + x)   5*x*(-1 + x)\ |                               /  1        5  \   3*(-1 + x) *(-3 + 2*x)     30*x*(-1 + x)     30*x*(-1 + x) *(-3 + 2*x)   6*x*(-1 + x) *(-3 + 2*x)   9*x*(-1 + x)*(-3 + 2*x)|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                |
      ___________________ |            3*x*(-1 + x)*(-3 + 2*x)   9 - 12*x - (-1 + x) *(-1 + 4*x)*|--------- + -------- + ----------------| + --------------------- + 3*(-1 + x)*(-1 + 2*x)*|------ + -----| + ---------------------- + ----------------- - ----------------- - ------------------ - ----------------------- - ---------------------- + ---------------------- + ----------------- - ------------------------- - ------------------------- + ------------------------ + ----------------------- + ------------------------- + ------------------------- + --------------------------      /          3*x*(-1 + x)*(-3 + 2*x)\     /          3*x*(-1 + x)*(-3 + 2*x)\   3*|6 - 12*x + (-1 + x)*(-1 + 4*x)*|------ + -----| + ---------------------- + ----------------- - ------------------------- - ------------------------ + -----------------------|   6 - 12*x + (-1 + x)*(-1 + 4*x)*|------ + -----| + ---------------------- + ----------------- - ------------------------- - ------------------------ + -----------------------             3*x*(-1 + x)*(-3 + 2*x)   6 - 12*x + (-1 + x)*(-1 + 4*x)*|------ + -----| + ---------------------- + ----------------- - ------------------------- - ------------------------ + -----------------------   5*|6 - 12*x + (-1 + x)*(-1 + 4*x)*|------ + -----| + ---------------------- + ----------------- - ------------------------- - ------------------------ + -----------------------|     /          3*x*(-1 + x)*(-3 + 2*x)\     /          3*x*(-1 + x)*(-3 + 2*x)\     /          3*x*(-1 + x)*(-3 + 2*x)\     /          3*x*(-1 + x)*(-3 + 2*x)\      /          3*x*(-1 + x)*(-3 + 2*x)\   /          3*x*(-1 + x)*(-3 + 2*x)\ /                      /  1        5  \\     /          3*x*(-1 + x)*(-3 + 2*x)\ /          x*(-1 + x)   5*x*(-1 + x)\   |-1 + 4*x - x*(-1 + x)*|------ + -----||*|6 - 12*x + (-1 + x)*(-1 + 4*x)*|------ + -----| + ---------------------- + ----------------- - ------------------------- - ------------------------ + -----------------------|   /          3*x*(-1 + x)*(-3 + 2*x)\ /          x*(-1 + x)   5*x*(-1 + x)\   |1 - 4*x + -----------------------|*|6 - 12*x + --------- + (-1 + x) *|------ + -----| + ----------- - 2*x*(-1 + x) *|--------- + -------- + ----------------| + ------------ + 3*x*(-1 + x)*|------ + -----| + -------------|   |1 - 4*x + ---------- + ------------|*|6 - 12*x + (-1 + x)*(-1 + 4*x)*|------ + -----| + ---------------------- + ----------------- - ------------------------- - ------------------------ + -----------------------|     /          3*x*(-1 + x)*(-3 + 2*x)\ /                      /  1        5  \\     /          3*x*(-1 + x)*(-3 + 2*x)\ /                      /  1        5  \\   /          3*x*(-1 + x)*(-3 + 2*x)\ /                      /  1        5  \\   /          3*x*(-1 + x)*(-3 + 2*x)\ /          x*(-1 + x)   5*x*(-1 + x)\   /          3*x*(-1 + x)*(-3 + 2*x)\ /                      /  1        5  \\ /          x*(-1 + x)   5*x*(-1 + x)\     /          3*x*(-1 + x)*(-3 + 2*x)\ /          x*(-1 + x)   5*x*(-1 + x)\|
     /              3     |  1 - 4*x + -----------------------                                   |        2          2   (1 + x)*(-2 + x)|           -2 + x                                \-2 + x   1 + x/           1 + x                   2                   3                   2         2             2                                 2         (1 + x)*(-2 + x)             2                       2                                    2                          3           (1 + x)*(-2 + x)                 3                           2         2                 3                 10*|1 - 4*x + -----------------------|   6*|1 - 4*x + -----------------------|     |                               \-2 + x   1 + x/      (1 + x)*(-2 + x)             2                       2                                   2           (1 + x)*(-2 + x)   |                                  \-2 + x   1 + x/      (1 + x)*(-2 + x)             2                       2                                   2           (1 + x)*(-2 + x)      1 - 4*x + -----------------------                                  \-2 + x   1 + x/      (1 + x)*(-2 + x)             2                       2                                   2           (1 + x)*(-2 + x)        |                               \-2 + x   1 + x/      (1 + x)*(-2 + x)             2                       2                                   2           (1 + x)*(-2 + x)   |   5*|1 - 4*x + -----------------------|   3*|1 - 4*x + -----------------------|   3*|1 - 4*x + -----------------------|   5*|1 - 4*x + -----------------------|   15*|1 - 4*x + -----------------------|   |1 - 4*x + -----------------------|*|-1 + 4*x - x*(-1 + x)*|------ + -----||   3*|1 - 4*x + -----------------------|*|1 - 4*x + ---------- + ------------|   \                      \-2 + x   1 + x// |                               \-2 + x   1 + x/      (1 + x)*(-2 + x)             2                       2                                   2           (1 + x)*(-2 + x)   |   |1 - 4*x + -----------------------|*|1 - 4*x + ---------- + ------------|   \              (1 + x)*(-2 + x)   / |             -2 + x              \-2 + x   1 + x/      1 + x                    |        2          2   (1 + x)*(-2 + x)|      -2 + x                   \-2 + x   1 + x/       1 + x    |   \            -2 + x        1 + x    / |                               \-2 + x   1 + x/      (1 + x)*(-2 + x)             2                       2                                   2           (1 + x)*(-2 + x)   |   3*|1 - 4*x + -----------------------|*|-1 + 4*x - x*(-1 + x)*|------ + -----||   5*|1 - 4*x + -----------------------|*|-1 + 4*x - x*(-1 + x)*|------ + -----||   |1 - 4*x + -----------------------|*|-1 + 4*x - x*(-1 + x)*|------ + -----||   |1 - 4*x + -----------------------|*|1 - 4*x + ---------- + ------------|   |1 - 4*x + -----------------------|*|-1 + 4*x - x*(-1 + x)*|------ + -----||*|1 - 4*x + ---------- + ------------|   5*|1 - 4*x + -----------------------|*|1 - 4*x + ---------- + ------------||
    /     x*(-1 + x)      |                (1 + x)*(-2 + x)                                      \(-2 + x)    (1 + x)                    /                                                                                             (1 + x) *(-2 + x)   (1 + x) *(-2 + x)   (1 + x) *(-2 + x)       (1 + x) *(-2 + x)        (1 + x)*(-2 + x)                                (1 + x) *(-2 + x)       (1 + x) *(-2 + x)           (1 + x)*(-2 + x)           (1 + x)*(-2 + x)                                      (1 + x) *(-2 + x)           (1 + x) *(-2 + x)           (1 + x) *(-2 + x)           \              (1 + x)*(-2 + x)   /     \              (1 + x)*(-2 + x)   /     \                                                                           (1 + x) *(-2 + x)       (1 + x) *(-2 + x)          (1 + x)*(-2 + x)                               /                                                                              (1 + x) *(-2 + x)       (1 + x) *(-2 + x)          (1 + x)*(-2 + x)                                                (1 + x)*(-2 + x)                                                                                 (1 + x) *(-2 + x)       (1 + x) *(-2 + x)          (1 + x)*(-2 + x)                                    \                                                                           (1 + x) *(-2 + x)       (1 + x) *(-2 + x)          (1 + x)*(-2 + x)                               /     \              (1 + x)*(-2 + x)   /     \              (1 + x)*(-2 + x)   /     \              (1 + x)*(-2 + x)   /     \              (1 + x)*(-2 + x)   /      \              (1 + x)*(-2 + x)   /   \              (1 + x)*(-2 + x)   / \                      \-2 + x   1 + x//     \              (1 + x)*(-2 + x)   / \            -2 + x        1 + x    /                                            \                                                                           (1 + x) *(-2 + x)       (1 + x) *(-2 + x)          (1 + x)*(-2 + x)                               /   \              (1 + x)*(-2 + x)   / \            -2 + x        1 + x    /                                       \                                                                                \(-2 + x)    (1 + x)                    /                                                               /                                         \                                                                           (1 + x) *(-2 + x)       (1 + x) *(-2 + x)          (1 + x)*(-2 + x)                               /     \              (1 + x)*(-2 + x)   / \                      \-2 + x   1 + x//     \              (1 + x)*(-2 + x)   / \                      \-2 + x   1 + x//   \              (1 + x)*(-2 + x)   / \                      \-2 + x   1 + x//   \              (1 + x)*(-2 + x)   / \            -2 + x        1 + x    /   \              (1 + x)*(-2 + x)   / \                      \-2 + x   1 + x// \            -2 + x        1 + x    /     \              (1 + x)*(-2 + x)   / \            -2 + x        1 + x    /|
   /   ----------------- *|- --------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------- - ------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------- - ------------------------------------- + ------------------------------------- + ------------------------------------- + -------------------------------------- + ---------------------------------------------------------------------------- - --------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------ - ------------------------------------------------------------------------------ - ---------------------------------------------------------------------------- + ------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------ + ---------------------------------------------------------------------------|
  /           5           |                   2                                                                                                                                                                                                                                                                                      2                                                                                                                                                                                                                                                                                      2                                        2                                                                                                             2                                                                                                                                                                         x*(-1 + x)                                                                                                x*(-2 + x)                                                                                            (-1 + x)*(-2 + x)                                                                                                                                                                  (1 + x)*(-1 + x)                                                                                              (1 + x)*(-2 + x)                           x*(-1 + x)                          (-1 + x)*(-2 + x)                           x*(1 + x)                            (1 + x)*(-1 + x)                                                2                                                                                       2                                                                                                                                                   2                                                                                                                                          2                                                                                                                                                              2                                                                                                                                                                                                                            2                                                                                                                                                   2                                                                 2*x*(1 + x)*(-1 + x)                                                           2*x*(-1 + x)*(-2 + x)                                                         4*x*(-1 + x)*(-2 + x)                                                                                  2         2                                                                                 4*x*(1 + x)*(-1 + x)                           |
\/     (1 + x) *(-2 + x)  \                  x                                                                                                                                                                                                                                                                               (-1 + x)                                                                                                                                                                                                                                                                                (1 + x)                                 (-1 + x)                                                                                                      (-1 + x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        2*x *(-1 + x)                                                                  4*x*(-1 + x)                                                                                                                                        4*x*(-1 + x)                                                                                                                                        4*x *(-1 + x)                                                                                                                                         4*x*(-1 + x)                                                                                                                                                                                                                 4*x*(-1 + x)                                                                                                                                        2*x*(-1 + x)                                                                                                                                                                                                                                                                                                                                   8*x *(-1 + x)                                                                                                                                 /
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$$\frac{\sqrt{\frac{x \left(x - 1\right)^{3}}{\left(x - 2\right) \left(x + 1\right)^{5}}} \left(- \frac{10 \left(- 4 x + \frac{3 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} + 1\right)}{\left(x + 1\right)^{2}} + \frac{15 \left(- 4 x + \frac{3 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} + 1\right)}{\left(x - 1\right) \left(x + 1\right)} - \frac{5 \left(- 12 x + \frac{30 x \left(x - 1\right)^{3}}{\left(x - 2\right) \left(x + 1\right)^{2}} - \frac{30 x \left(x - 1\right)^{2} \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)^{2}} + \frac{9 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} - \frac{6 x \left(x - 1\right)^{2} \left(2 x - 3\right)}{\left(x - 2\right)^{2} \left(x + 1\right)} + \left(x - 1\right) \left(4 x - 1\right) \left(\frac{5}{x + 1} + \frac{1}{x - 2}\right) + 6 + \frac{3 \left(x - 1\right)^{2} \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)}\right)}{\left(x - 1\right) \left(x + 1\right)} - \frac{6 \left(- 4 x + \frac{3 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} + 1\right)}{\left(x - 1\right)^{2}} + \frac{3 \left(- 12 x + \frac{30 x \left(x - 1\right)^{3}}{\left(x - 2\right) \left(x + 1\right)^{2}} - \frac{30 x \left(x - 1\right)^{2} \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)^{2}} + \frac{9 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} - \frac{6 x \left(x - 1\right)^{2} \left(2 x - 3\right)}{\left(x - 2\right)^{2} \left(x + 1\right)} + \left(x - 1\right) \left(4 x - 1\right) \left(\frac{5}{x + 1} + \frac{1}{x - 2}\right) + 6 + \frac{3 \left(x - 1\right)^{2} \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)}\right)}{\left(x - 1\right)^{2}} - \frac{- 12 x - \frac{300 x \left(x - 1\right)^{4}}{\left(x - 2\right) \left(x + 1\right)^{3}} + \frac{90 x \left(x - 1\right)^{3}}{\left(x - 2\right) \left(x + 1\right)^{2}} + \frac{165 x \left(x - 1\right)^{3} \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)^{3}} + \frac{30 x \left(x - 1\right)^{3} \left(2 x - 1\right)}{\left(x - 2\right) \left(x + 1\right)^{3}} - \frac{90 x \left(x - 1\right)^{2} \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)^{2}} + \frac{9 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} - \frac{60 x \left(x - 1\right)^{4}}{\left(x - 2\right)^{2} \left(x + 1\right)^{2}} + \frac{60 x \left(x - 1\right)^{3} \left(2 x - 3\right)}{\left(x - 2\right)^{2} \left(x + 1\right)^{2}} - \frac{18 x \left(x - 1\right)^{2} \left(2 x - 3\right)}{\left(x - 2\right)^{2} \left(x + 1\right)} + \frac{9 x \left(x - 1\right)^{3} \left(2 x - 3\right)}{\left(x - 2\right)^{3} \left(x + 1\right)} - \left(x - 1\right)^{2} \left(4 x - 1\right) \left(\frac{15}{\left(x + 1\right)^{2}} + \frac{5}{\left(x - 2\right) \left(x + 1\right)} + \frac{1}{\left(x - 2\right)^{2}}\right) + 3 \left(x - 1\right) \left(2 x - 1\right) \left(\frac{5}{x + 1} + \frac{1}{x - 2}\right) + \frac{15 \left(x - 1\right) \left(2 x - 1\right)}{x + 1} + 9 + \frac{30 \left(x - 1\right)^{4}}{\left(x - 2\right) \left(x + 1\right)^{2}} - \frac{30 \left(x - 1\right)^{3} \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)^{2}} + \frac{9 \left(x - 1\right)^{2} \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} + \frac{3 \left(x - 1\right) \left(2 x - 1\right)}{x - 2} - \frac{6 \left(x - 1\right)^{3} \left(2 x - 3\right)}{\left(x - 2\right)^{2} \left(x + 1\right)}}{\left(x - 1\right)^{2}} - \frac{5 \left(- 4 x + \frac{3 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} + 1\right)}{\left(x - 2\right) \left(x + 1\right)} + \frac{3 \left(- 4 x + \frac{3 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} + 1\right)}{\left(x - 2\right) \left(x - 1\right)} - \frac{- 12 x + \frac{30 x \left(x - 1\right)^{3}}{\left(x - 2\right) \left(x + 1\right)^{2}} - \frac{30 x \left(x - 1\right)^{2} \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)^{2}} + \frac{9 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} - \frac{6 x \left(x - 1\right)^{2} \left(2 x - 3\right)}{\left(x - 2\right)^{2} \left(x + 1\right)} + \left(x - 1\right) \left(4 x - 1\right) \left(\frac{5}{x + 1} + \frac{1}{x - 2}\right) + 6 + \frac{3 \left(x - 1\right)^{2} \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)}}{\left(x - 2\right) \left(x - 1\right)} + \frac{5 \left(- 4 x + \frac{3 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} + 1\right)}{x \left(x + 1\right)} - \frac{3 \left(- 4 x + \frac{3 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} + 1\right)}{x \left(x - 1\right)} + \frac{- 12 x + \frac{30 x \left(x - 1\right)^{3}}{\left(x - 2\right) \left(x + 1\right)^{2}} - \frac{30 x \left(x - 1\right)^{2} \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)^{2}} + \frac{9 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} - \frac{6 x \left(x - 1\right)^{2} \left(2 x - 3\right)}{\left(x - 2\right)^{2} \left(x + 1\right)} + \left(x - 1\right) \left(4 x - 1\right) \left(\frac{5}{x + 1} + \frac{1}{x - 2}\right) + 6 + \frac{3 \left(x - 1\right)^{2} \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)}}{x \left(x - 1\right)} - \frac{5 \left(- 4 x + \frac{3 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} + 1\right) \left(- x \left(x - 1\right) \left(\frac{5}{x + 1} + \frac{1}{x - 2}\right) + 4 x - 1\right)}{2 x \left(x - 1\right) \left(x + 1\right)} + \frac{5 \left(- 4 x + \frac{3 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} + 1\right) \left(\frac{5 x \left(x - 1\right)}{x + 1} - 4 x + \frac{x \left(x - 1\right)}{x - 2} + 1\right)}{4 x \left(x - 1\right) \left(x + 1\right)} + \frac{3 \left(- 4 x + \frac{3 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} + 1\right) \left(- x \left(x - 1\right) \left(\frac{5}{x + 1} + \frac{1}{x - 2}\right) + 4 x - 1\right)}{2 x \left(x - 1\right)^{2}} - \frac{3 \left(- 4 x + \frac{3 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} + 1\right) \left(\frac{5 x \left(x - 1\right)}{x + 1} - 4 x + \frac{x \left(x - 1\right)}{x - 2} + 1\right)}{4 x \left(x - 1\right)^{2}} + \frac{\left(- 4 x + \frac{3 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} + 1\right) \left(- 2 x \left(x - 1\right)^{2} \left(\frac{15}{\left(x + 1\right)^{2}} + \frac{5}{\left(x - 2\right) \left(x + 1\right)} + \frac{1}{\left(x - 2\right)^{2}}\right) + 3 x \left(x - 1\right) \left(\frac{5}{x + 1} + \frac{1}{x - 2}\right) + \frac{15 x \left(x - 1\right)}{x + 1} - 12 x + \frac{3 x \left(x - 1\right)}{x - 2} + \left(x - 1\right)^{2} \left(\frac{5}{x + 1} + \frac{1}{x - 2}\right) + \frac{5 \left(x - 1\right)^{2}}{x + 1} + 6 + \frac{\left(x - 1\right)^{2}}{x - 2}\right)}{4 x \left(x - 1\right)^{2}} - \frac{\left(- x \left(x - 1\right) \left(\frac{5}{x + 1} + \frac{1}{x - 2}\right) + 4 x - 1\right) \left(- 12 x + \frac{30 x \left(x - 1\right)^{3}}{\left(x - 2\right) \left(x + 1\right)^{2}} - \frac{30 x \left(x - 1\right)^{2} \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)^{2}} + \frac{9 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} - \frac{6 x \left(x - 1\right)^{2} \left(2 x - 3\right)}{\left(x - 2\right)^{2} \left(x + 1\right)} + \left(x - 1\right) \left(4 x - 1\right) \left(\frac{5}{x + 1} + \frac{1}{x - 2}\right) + 6 + \frac{3 \left(x - 1\right)^{2} \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)}\right)}{4 x \left(x - 1\right)^{2}} + \frac{\left(\frac{5 x \left(x - 1\right)}{x + 1} - 4 x + \frac{x \left(x - 1\right)}{x - 2} + 1\right) \left(- 12 x + \frac{30 x \left(x - 1\right)^{3}}{\left(x - 2\right) \left(x + 1\right)^{2}} - \frac{30 x \left(x - 1\right)^{2} \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)^{2}} + \frac{9 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} - \frac{6 x \left(x - 1\right)^{2} \left(2 x - 3\right)}{\left(x - 2\right)^{2} \left(x + 1\right)} + \left(x - 1\right) \left(4 x - 1\right) \left(\frac{5}{x + 1} + \frac{1}{x - 2}\right) + 6 + \frac{3 \left(x - 1\right)^{2} \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)}\right)}{4 x \left(x - 1\right)^{2}} + \frac{- 4 x + \frac{3 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} + 1}{x \left(x - 2\right)} - \frac{\left(- 4 x + \frac{3 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} + 1\right) \left(- x \left(x - 1\right) \left(\frac{5}{x + 1} + \frac{1}{x - 2}\right) + 4 x - 1\right)}{2 x \left(x - 2\right) \left(x - 1\right)} + \frac{\left(- 4 x + \frac{3 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} + 1\right) \left(\frac{5 x \left(x - 1\right)}{x + 1} - 4 x + \frac{x \left(x - 1\right)}{x - 2} + 1\right)}{4 x \left(x - 2\right) \left(x - 1\right)} - \frac{- 4 x + \frac{3 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} + 1}{x^{2}} + \frac{\left(- 4 x + \frac{3 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} + 1\right) \left(- x \left(x - 1\right) \left(\frac{5}{x + 1} + \frac{1}{x - 2}\right) + 4 x - 1\right)}{2 x^{2} \left(x - 1\right)} - \frac{\left(- 4 x + \frac{3 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} + 1\right) \left(\frac{5 x \left(x - 1\right)}{x + 1} - 4 x + \frac{x \left(x - 1\right)}{x - 2} + 1\right)}{4 x^{2} \left(x - 1\right)} + \frac{\left(- 4 x + \frac{3 x \left(x - 1\right) \left(2 x - 3\right)}{\left(x - 2\right) \left(x + 1\right)} + 1\right) \left(- x \left(x - 1\right) \left(\frac{5}{x + 1} + \frac{1}{x - 2}\right) + 4 x - 1\right) \left(\frac{5 x \left(x - 1\right)}{x + 1} - 4 x + \frac{x \left(x - 1\right)}{x - 2} + 1\right)}{8 x^{2} \left(x - 1\right)^{2}}\right)}{x \left(x - 1\right)}$$

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Gráfico

Derivada de ((x*(x-1)^3)/(((x+1)^5)*(x-2)))^1/2

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Derivada de ((x(x-1)^3)/(((x+1)^5)(x-2)))^1/2

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Solución

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Derivada de ((x*(x-1)^3)/(((x+1)^5)*(x-2)))^1/2

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Solución

Derivada de ((x(x-1)^3)/(((x+1)^5)(x-2)))^1/2