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Derivada de:
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Expresiones idénticas
y=x^ tres *sqrt((x- uno)/((x+ dos)*sqrt(x- dos)))
y es igual a x al cubo multiplicar por raíz cuadrada de ((x menos 1) dividir por ((x más 2) multiplicar por raíz cuadrada de (x menos 2)))
y es igual a x en el grado tres multiplicar por raíz cuadrada de ((x menos uno) dividir por ((x más dos) multiplicar por raíz cuadrada de (x menos dos)))
y=x^3*√((x-1)/((x+2)*√(x-2)))
y=x3*sqrt((x-1)/((x+2)*sqrt(x-2)))
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y=x en el grado 3*sqrt((x-1)/((x+2)*sqrt(x-2)))
y=x^3sqrt((x-1)/((x+2)sqrt(x-2)))
y=x3sqrt((x-1)/((x+2)sqrt(x-2)))
y=x3sqrtx-1/x+2sqrtx-2
y=x^3sqrtx-1/x+2sqrtx-2
y=x^3*sqrt((x-1) dividir por ((x+2)*sqrt(x-2)))
Expresiones semejantes
y=x^3*sqrt((x-1)/((x+2)*sqrt(x+2)))
y=x^3*sqrt((x-1)/((x-2)*sqrt(x-2)))
y=x^3*sqrt((x+1)/((x+2)*sqrt(x-2)))
Expresiones con funciones
Raíz cuadrada sqrt
sqrt(x^2+16)+3x
sqrt(5*x+1)
sqrt(sinx^3)
sqrt(log(6*x-1))
sqrt(x)-1/sqrt(x)
Raíz cuadrada sqrt
sqrt(x^2+16)+3x
sqrt(5*x+1)
sqrt(sinx^3)
sqrt(log(6*x-1))
sqrt(x)-1/sqrt(x)

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

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

Solución

Ha introducido [src]

        ___________________
 3     /       x - 1       
x *   /  ----------------- 
     /             _______ 
   \/    (x + 2)*\/ x - 2

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

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

Solución detallada

Se aplica la regla de la derivada de una multiplicación:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

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

$\frac{x^{2} \left(11 x^{3} - 7 x^{2} - 58 x + 48\right)}{4 \sqrt{\frac{x - 1}{\sqrt{x - 2} \left(x + 2\right)}} \sqrt{x - 2} \left(x^{3} + 2 x^{2} - 4 x - 8\right)}$

Respuesta:

$\frac{x^{2} \left(11 x^{3} - 7 x^{2} - 58 x + 48\right)}{4 \sqrt{\frac{x - 1}{\sqrt{x - 2} \left(x + 2\right)}} \sqrt{x - 2} \left(x^{3} + 2 x^{2} - 4 x - 8\right)}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

                                                                                      //        1        \           /    _______      x + 2   \\
                                                                                      ||-----------------|   (x - 1)*|- \/ x - 2  - -----------||
                                                ___________________                   ||  _______        |           |                  _______||
                                         3     /       x - 1          _______         |\\/ x - 2 *(x + 2)/           \              2*\/ x - 2 /|
                                        x *   /  ----------------- *\/ x - 2 *(x + 2)*|------------------- + -----------------------------------|
          ___________________________        /     _______                            |         2                                      2        |
   2     /         1                       \/    \/ x - 2 *(x + 2)                    \                               2*(x - 2)*(x + 2)         /
3*x *   /  -----------------*(x - 1)  + ---------------------------------------------------------------------------------------------------------
       /     _______                                                                      x - 1                                                  
     \/    \/ x - 2 *(x + 2)

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

Simplificar

Segunda derivada [src]

                            /       /                                                                                                                                                                                              /                        /    ________     2 + x   \\                /                        /    ________     2 + x   \\                /                        /    ________     2 + x   \\                                               /                        /    ________     2 + x   \\\                                                                       \
                            |       |                                                                                                                                                                                              |               (-1 + x)*|2*\/ -2 + x  + ----------||                |               (-1 + x)*|2*\/ -2 + x  + ----------||                |               (-1 + x)*|2*\/ -2 + x  + ----------||                                               |               (-1 + x)*|2*\/ -2 + x  + ----------|||                                                                       |
                            |       |                                                                                                                                                                                              |                        |                 ________||                |                        |                 ________||                |                        |                 ________||                                               |                        |                 ________|||                                                                       |
                            |       |             /                                     /    ________     2 + x   \                                      /    ________     2 + x   \              /    ________     2 + x   \\     |      2                 \               \/ -2 + x /|       ________ |      2                 \               \/ -2 + x /|       ________ |      2                 \               \/ -2 + x /|     ________ /              /  1        2  \\ |      2                 \               \/ -2 + x /||                  /                        /    ________     2 + x   \\|
                            |       |             |                                   2*|2*\/ -2 + x  + ----------|            /    2 + x \   4*(-1 + x)*|2*\/ -2 + x  + ----------|   2*(-1 + x)*|2*\/ -2 + x  + ----------||   2*|- ---------- + ------------------------------------|   4*\/ -2 + x *|- ---------- + ------------------------------------|   4*\/ -2 + x *|- ---------- + ------------------------------------|   \/ -2 + x *|-2 + (-1 + x)*|------ + -----||*|- ---------- + ------------------------------------||                  |               (-1 + x)*|2*\/ -2 + x  + ----------|||
                            |       |             |                                     |                 ________|   (-1 + x)*|4 - ------|              |                 ________|              |                 ________||     |    ________             (-2 + x)*(2 + x)          |                |    ________             (-2 + x)*(2 + x)          |                |    ________             (-2 + x)*(2 + x)          |              \              \-2 + x   2 + x// |    ________             (-2 + x)*(2 + x)          ||                  |                        |                 ________|||
                            |     2 |    ________ |     2                4              \               \/ -2 + x /            \    -2 + x/              \               \/ -2 + x /              \               \/ -2 + x /|     \  \/ -2 + x                                        /                \  \/ -2 + x                                        /                \  \/ -2 + x                                        /                                               \  \/ -2 + x                                        /|         ________ |      2                 \               \/ -2 + x /||
                            |    x *|2*\/ -2 + x *|----------- + ------------------ + ----------------------------- + --------------------- - -------------------------------------- - --------------------------------------| + ------------------------------------------------------- - ------------------------------------------------------------------ + ------------------------------------------------------------------ - -------------------------------------------------------------------------------------------------|   3*x*\/ -2 + x *|- ---------- + ------------------------------------||
       ____________________ |       |             |        3/2     ________                  (-2 + x)*(2 + x)                  3/2                                      2                                2                   |                            ________                                                       -1 + x                                                               2 + x                                                                                -1 + x                                             |                  |    ________             (-2 + x)*(2 + x)          ||
      /       -1 + x        |       \             \(-2 + x)      \/ -2 + x *(2 + x)                                    (-2 + x)   *(2 + x)              (-2 + x)*(2 + x)                         (-2 + x) *(2 + x)           /                          \/ -2 + x                                                                                                                                                                                                                                                                     /                  \  \/ -2 + x                                        /|
x*   /  ------------------ *|6 - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - --------------------------------------------------------------------|
    /     ________          \                                                                                                                                                                                                                                                 16*(-1 + x)                                                                                                                                                                                                                                                                              2*(-1 + x)                             /
  \/    \/ -2 + x *(2 + x)

$$x \sqrt{\frac{x - 1}{\sqrt{x - 2} \left(x + 2\right)}} \left(- \frac{x^{2} \left(2 \sqrt{x - 2} \left(\frac{\left(4 - \frac{x + 2}{x - 2}\right) \left(x - 1\right)}{\left(x - 2\right)^{\frac{3}{2}} \left(x + 2\right)} - \frac{4 \left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)^{2}} + \frac{2 \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2 \left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right)^{2} \left(x + 2\right)} + \frac{4}{\sqrt{x - 2} \left(x + 2\right)} + \frac{2}{\left(x - 2\right)^{\frac{3}{2}}}\right) + \frac{4 \sqrt{x - 2} \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right)}{x + 2} - \frac{\sqrt{x - 2} \left(\left(x - 1\right) \left(\frac{2}{x + 2} + \frac{1}{x - 2}\right) - 2\right) \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right)}{x - 1} - \frac{4 \sqrt{x - 2} \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right)}{x - 1} + \frac{2 \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right)}{\sqrt{x - 2}}\right)}{16 \left(x - 1\right)} - \frac{3 x \sqrt{x - 2} \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right)}{2 \left(x - 1\right)} + 6\right)$$

Simplificar

Tercera derivada [src]

                          /         /                                                                                                                                                                                              /                        /    ________     2 + x   \\                /                        /    ________     2 + x   \\                /                        /    ________     2 + x   \\                                               /                        /    ________     2 + x   \\\      /    /                                     /    ________     2 + x   \                                      /    ________     2 + x   \              /    ________     2 + x   \\                                                                                                                                                                                                                                                                                                                                                                                /                        /    ________     2 + x   \\                 /                        /    ________     2 + x   \\                 /                                     /    ________     2 + x   \                                      /    ________     2 + x   \              /    ________     2 + x   \\      /                        /    ________     2 + x   \\                 /                                     /    ________     2 + x   \                                      /    ________     2 + x   \              /    ________     2 + x   \\      /                        /    ________     2 + x   \\                                                 /                        /    ________     2 + x   \\                /                        /    ________     2 + x   \\                                                                            /                                     /    ________     2 + x   \                                      /    ________     2 + x   \              /    ________     2 + x   \\                /                        /    ________     2 + x   \\                                                                                                                 /                                     /    ________     2 + x   \                                      /    ________     2 + x   \              /    ________     2 + x   \\     /                        /    ________     2 + x   \\                                                                 /                        /    ________     2 + x   \\                 /                        /    ________     2 + x   \\                                               /                        /    ________     2 + x   \\                                           /                        /    ________     2 + x   \\                                                                            /                        /    ________     2 + x   \\\                                                                       \
                          |         |                                                                                                                                                                                              |               (-1 + x)*|2*\/ -2 + x  + ----------||                |               (-1 + x)*|2*\/ -2 + x  + ----------||                |               (-1 + x)*|2*\/ -2 + x  + ----------||                                               |               (-1 + x)*|2*\/ -2 + x  + ----------|||      |    |                                   2*|2*\/ -2 + x  + ----------|            /    2 + x \   4*(-1 + x)*|2*\/ -2 + x  + ----------|   2*(-1 + x)*|2*\/ -2 + x  + ----------||                                                                                                                                                                                                                                                                                                                                                                                |               (-1 + x)*|2*\/ -2 + x  + ----------||                 |               (-1 + x)*|2*\/ -2 + x  + ----------||                 |                                   2*|2*\/ -2 + x  + ----------|            /    2 + x \   4*(-1 + x)*|2*\/ -2 + x  + ----------|   2*(-1 + x)*|2*\/ -2 + x  + ----------||      |               (-1 + x)*|2*\/ -2 + x  + ----------||                 |                                   2*|2*\/ -2 + x  + ----------|            /    2 + x \   4*(-1 + x)*|2*\/ -2 + x  + ----------|   2*(-1 + x)*|2*\/ -2 + x  + ----------||      |               (-1 + x)*|2*\/ -2 + x  + ----------||                                                 |               (-1 + x)*|2*\/ -2 + x  + ----------||                |               (-1 + x)*|2*\/ -2 + x  + ----------||                                                                            |                                   2*|2*\/ -2 + x  + ----------|            /    2 + x \   4*(-1 + x)*|2*\/ -2 + x  + ----------|   2*(-1 + x)*|2*\/ -2 + x  + ----------||                |               (-1 + x)*|2*\/ -2 + x  + ----------||                                                                                                                 |                                   2*|2*\/ -2 + x  + ----------|            /    2 + x \   4*(-1 + x)*|2*\/ -2 + x  + ----------|   2*(-1 + x)*|2*\/ -2 + x  + ----------||     |               (-1 + x)*|2*\/ -2 + x  + ----------||                                                                 |               (-1 + x)*|2*\/ -2 + x  + ----------||                 |               (-1 + x)*|2*\/ -2 + x  + ----------||                                               |               (-1 + x)*|2*\/ -2 + x  + ----------||                                           |               (-1 + x)*|2*\/ -2 + x  + ----------||                                                                            |               (-1 + x)*|2*\/ -2 + x  + ----------|||                                                                       |
                          |         |                                                                                                                                                                                              |                        |                 ________||                |                        |                 ________||                |                        |                 ________||                                               |                        |                 ________|||      |    |                                     |                 ________|   (-1 + x)*|4 - ------|              |                 ________|              |                 ________||                                                                                                                                                                                                                                                                                                                                                                                |                        |                 ________||                 |                        |                 ________||                 |                                     |                 ________|   (-1 + x)*|4 - ------|              |                 ________|              |                 ________||      |                        |                 ________||                 |                                     |                 ________|   (-1 + x)*|4 - ------|              |                 ________|              |                 ________||      |                        |                 ________||                                                 |                        |                 ________||                |                        |                 ________||                                                                            |                                     |                 ________|   (-1 + x)*|4 - ------|              |                 ________|              |                 ________||                |                        |                 ________||                                                                                                                 |                                     |                 ________|   (-1 + x)*|4 - ------|              |                 ________|              |                 ________||     |                        |                 ________||                                                                 |                        |                 ________||                 |                        |                 ________||                                               |                        |                 ________||                                           |                        |                 ________||                                                                            |                        |                 ________|||                                                                       |
                          |         |             /                                     /    ________     2 + x   \                                      /    ________     2 + x   \              /    ________     2 + x   \\     |      2                 \               \/ -2 + x /|       ________ |      2                 \               \/ -2 + x /|       ________ |      2                 \               \/ -2 + x /|     ________ /              /  1        2  \\ |      2                 \               \/ -2 + x /||      |    |     2                4              \               \/ -2 + x /            \    -2 + x/              \               \/ -2 + x /              \               \/ -2 + x /|                /                                                                                  /    ________     2 + x   \      /    ________     2 + x   \               /    ________     2 + x   \               /    ________     2 + x   \              /    ________     2 + x   \                                                                              \     |      2                 \               \/ -2 + x /|        ________ |      2                 \               \/ -2 + x /|        ________ |     2                4              \               \/ -2 + x /            \    -2 + x/              \               \/ -2 + x /              \               \/ -2 + x /|      |      2                 \               \/ -2 + x /|        ________ |     2                4              \               \/ -2 + x /            \    -2 + x/              \               \/ -2 + x /              \               \/ -2 + x /|      |      2                 \               \/ -2 + x /|       ________ /              /  1        2  \\ |      2                 \               \/ -2 + x /|       ________ |      2                 \               \/ -2 + x /| /     -1 + x   2*(-1 + x)\       ________ /              /  1        2  \\ |     2                4              \               \/ -2 + x /            \    -2 + x/              \               \/ -2 + x /              \               \/ -2 + x /|       ________ |      2                 \               \/ -2 + x /| /  4        8              /    3          8              4        \\       ________ /     -1 + x   2*(-1 + x)\ |     2                4              \               \/ -2 + x /            \    -2 + x/              \               \/ -2 + x /              \               \/ -2 + x /|     |      2                 \               \/ -2 + x /| /     -1 + x   2*(-1 + x)\     /              /  1        2  \\ |      2                 \               \/ -2 + x /|        ________ |      2                 \               \/ -2 + x /|     ________ /              /  1        2  \\ |      2                 \               \/ -2 + x /| /     -1 + x   2*(-1 + x)\       ________ |      2                 \               \/ -2 + x /| /     -1 + x   2*(-1 + x)\       ________ /              /  1        2  \\ |      2                 \               \/ -2 + x /||                  /                        /    ________     2 + x   \\|
                          |         |             |                                   2*|2*\/ -2 + x  + ----------|            /    2 + x \   4*(-1 + x)*|2*\/ -2 + x  + ----------|   2*(-1 + x)*|2*\/ -2 + x  + ----------||   2*|- ---------- + ------------------------------------|   4*\/ -2 + x *|- ---------- + ------------------------------------|   4*\/ -2 + x *|- ---------- + ------------------------------------|   \/ -2 + x *|-2 + (-1 + x)*|------ + -----||*|- ---------- + ------------------------------------||      |  8*|----------- + ------------------ + ----------------------------- + --------------------- - -------------------------------------- - --------------------------------------|                |                                                               /    2 + x \     8*|2*\/ -2 + x  + ----------|   16*|2*\/ -2 + x  + ----------|   24*(-1 + x)*|2*\/ -2 + x  + ----------|   16*(-1 + x)*|2*\/ -2 + x  + ----------|   8*(-1 + x)*|2*\/ -2 + x  + ----------|              /    2 + x \              /    2 + x \              /    2 + x \|   4*|- ---------- + ------------------------------------|   32*\/ -2 + x *|- ---------- + ------------------------------------|   16*\/ -2 + x *|----------- + ------------------ + ----------------------------- + --------------------- - -------------------------------------- - --------------------------------------|   16*|- ---------- + ------------------------------------|   16*\/ -2 + x *|----------- + ------------------ + ----------------------------- + --------------------- - -------------------------------------- - --------------------------------------|   16*|- ---------- + ------------------------------------|   8*\/ -2 + x *|-2 + (-1 + x)*|------ + -----||*|- ---------- + ------------------------------------|   4*\/ -2 + x *|- ---------- + ------------------------------------|*|-2 + ------ + ----------|   2*\/ -2 + x *|-2 + (-1 + x)*|------ + -----||*|----------- + ------------------ + ----------------------------- + --------------------- - -------------------------------------- - --------------------------------------|   2*\/ -2 + x *|- ---------- + ------------------------------------|*|------ + ----- - (-1 + x)*|--------- + -------- + ----------------||   2*\/ -2 + x *|-2 + ------ + ----------|*|----------- + ------------------ + ----------------------------- + --------------------- - -------------------------------------- - --------------------------------------|   2*|- ---------- + ------------------------------------|*|-2 + ------ + ----------|   4*|-2 + (-1 + x)*|------ + -----||*|- ---------- + ------------------------------------|   32*\/ -2 + x *|- ---------- + ------------------------------------|   \/ -2 + x *|-2 + (-1 + x)*|------ + -----||*|- ---------- + ------------------------------------|*|-2 + ------ + ----------|   4*\/ -2 + x *|- ---------- + ------------------------------------|*|-2 + ------ + ----------|   8*\/ -2 + x *|-2 + (-1 + x)*|------ + -----||*|- ---------- + ------------------------------------||                  |               (-1 + x)*|2*\/ -2 + x  + ----------|||
                          |         |             |                                     |                 ________|   (-1 + x)*|4 - ------|              |                 ________|              |                 ________||     |    ________             (-2 + x)*(2 + x)          |                |    ________             (-2 + x)*(2 + x)          |                |    ________             (-2 + x)*(2 + x)          |              \              \-2 + x   2 + x// |    ________             (-2 + x)*(2 + x)          ||      |    |        3/2     ________                  (-2 + x)*(2 + x)                  3/2                                      2                                2                   |                |                                                             4*|4 - ------|       |                 ________|      |                 ________|               |                 ________|               |                 ________|              |                 ________|   3*(-1 + x)*|2 - ------|   4*(-1 + x)*|4 - ------|   8*(-1 + x)*|4 - ------||     |    ________             (-2 + x)*(2 + x)          |                 |    ________             (-2 + x)*(2 + x)          |                 |        3/2     ________                  (-2 + x)*(2 + x)                  3/2                                      2                                2                   |      |    ________             (-2 + x)*(2 + x)          |                 |        3/2     ________                  (-2 + x)*(2 + x)                  3/2                                      2                                2                   |      |    ________             (-2 + x)*(2 + x)          |                \              \-2 + x   2 + x// |    ________             (-2 + x)*(2 + x)          |                |    ________             (-2 + x)*(2 + x)          | \     -2 + x     2 + x   /                \              \-2 + x   2 + x// |        3/2     ________                  (-2 + x)*(2 + x)                  3/2                                      2                                2                   |                |    ________             (-2 + x)*(2 + x)          | |-2 + x   2 + x            |        2          2   (-2 + x)*(2 + x)||                \     -2 + x     2 + x   / |        3/2     ________                  (-2 + x)*(2 + x)                  3/2                                      2                                2                   |     |    ________             (-2 + x)*(2 + x)          | \     -2 + x     2 + x   /     \              \-2 + x   2 + x// |    ________             (-2 + x)*(2 + x)          |                 |    ________             (-2 + x)*(2 + x)          |              \              \-2 + x   2 + x// |    ________             (-2 + x)*(2 + x)          | \     -2 + x     2 + x   /                |    ________             (-2 + x)*(2 + x)          | \     -2 + x     2 + x   /                \              \-2 + x   2 + x// |    ________             (-2 + x)*(2 + x)          ||                  |                        |                 ________|||
                          |       2 |    ________ |     2                4              \               \/ -2 + x /            \    -2 + x/              \               \/ -2 + x /              \               \/ -2 + x /|     \  \/ -2 + x                                        /                \  \/ -2 + x                                        /                \  \/ -2 + x                                        /                                               \  \/ -2 + x                                        /|    3 |    \(-2 + x)      \/ -2 + x *(2 + x)                                    (-2 + x)   *(2 + x)              (-2 + x)*(2 + x)                         (-2 + x) *(2 + x)           /       ________ |     6                 8                     16                \    -2 + x/       \               \/ -2 + x /      \               \/ -2 + x /               \               \/ -2 + x /               \               \/ -2 + x /              \               \/ -2 + x /              \    -2 + x/              \    -2 + x/              \    -2 + x/|     \  \/ -2 + x                                        /                 \  \/ -2 + x                                        /                 \(-2 + x)      \/ -2 + x *(2 + x)                                    (-2 + x)   *(2 + x)              (-2 + x)*(2 + x)                         (-2 + x) *(2 + x)           /      \  \/ -2 + x                                        /                 \(-2 + x)      \/ -2 + x *(2 + x)                                    (-2 + x)   *(2 + x)              (-2 + x)*(2 + x)                         (-2 + x) *(2 + x)           /      \  \/ -2 + x                                        /                                                 \  \/ -2 + x                                        /                \  \/ -2 + x                                        /                                                                            \(-2 + x)      \/ -2 + x *(2 + x)                                    (-2 + x)   *(2 + x)              (-2 + x)*(2 + x)                         (-2 + x) *(2 + x)           /                \  \/ -2 + x                                        / \                          \(-2 + x)    (2 + x)                    //                                           \(-2 + x)      \/ -2 + x *(2 + x)                                    (-2 + x)   *(2 + x)              (-2 + x)*(2 + x)                         (-2 + x) *(2 + x)           /     \  \/ -2 + x                                        /                                                                 \  \/ -2 + x                                        /                 \  \/ -2 + x                                        /                                               \  \/ -2 + x                                        /                                           \  \/ -2 + x                                        /                                                                            \  \/ -2 + x                                        /|         ________ |      2                 \               \/ -2 + x /||
                          |    9*x *|2*\/ -2 + x *|----------- + ------------------ + ----------------------------- + --------------------- - -------------------------------------- - --------------------------------------| + ------------------------------------------------------- - ------------------------------------------------------------------ + ------------------------------------------------------------------ - -------------------------------------------------------------------------------------------------|   x *|- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + 4*\/ -2 + x *|----------- + ------------------- + ------------------- - ------------------- + ----------------------------- + ------------------------------ - --------------------------------------- - --------------------------------------- - -------------------------------------- + ----------------------- + ----------------------- + -----------------------| + ------------------------------------------------------- - ------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - -------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + -------------------------------------------------------- - --------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------- + ------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------|   9*x*\/ -2 + x *|- ---------- + ------------------------------------||
     ____________________ |         |             |        3/2     ________                  (-2 + x)*(2 + x)                  3/2                                      2                                2                   |                            ________                                                       -1 + x                                                               2 + x                                                                                -1 + x                                             |      |                                                                                      ________                                                                                                  |        5/2           3/2             ________        2           3/2                         2                                       2                                     3                                 2        2                               3                                5/2                       5/2                       3/2        2 |                                 3/2                                                              2                                                                                                                          2 + x                                                                                                                   ________                                                                                                                        -1 + x                                                                                                                          ________                                                                           2                                                                                                  2                                                                                                                                                       -1 + x                                                                                                                                                                              -1 + x                                                                                                                                                                           -1 + x                                                                                                                                                    ________                                                                                ________                                                                (-1 + x)*(2 + x)                                                                                             2                                                                                                    (-1 + x)*(2 + x)                                                                                   (-1 + x)*(2 + x)                                         |                  |    ________             (-2 + x)*(2 + x)          ||
    /       -1 + x        |         \             \(-2 + x)      \/ -2 + x *(2 + x)                                    (-2 + x)   *(2 + x)              (-2 + x)*(2 + x)                         (-2 + x) *(2 + x)           /                          \/ -2 + x                                                                                                                                                                                                                                                                     /      \                                                                                    \/ -2 + x                                                                                                   \(-2 + x)      (-2 + x)   *(2 + x)   \/ -2 + x *(2 + x)    (-2 + x)   *(2 + x)         (-2 + x) *(2 + x)               (-2 + x)*(2 + x)                      (-2 + x)*(2 + x)                          (-2 + x) *(2 + x)                        (-2 + x) *(2 + x)                (-2 + x)   *(2 + x)       (-2 + x)   *(2 + x)       (-2 + x)   *(2 + x)  /                         (-2 + x)                                                         (-1 + x)                                                                                                                                                                                                                                                 \/ -2 + x *(2 + x)                                                                                                                                                                                                                                     (-1 + x)*\/ -2 + x                                                                    (-1 + x)                                                                                           (-1 + x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            (-1 + x)*\/ -2 + x                                                                      (-1 + x)*\/ -2 + x                                                                                                                                                                      (-1 + x)                                                                                                                                                                                                                                                                 /                  \  \/ -2 + x                                        /|
   /  ------------------ *|6 - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------|
  /     ________          \                                                                                                                                                                                                                                                  16*(-1 + x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    64*(-1 + x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   2*(-1 + x)                             /
\/    \/ -2 + x *(2 + x)

$$\sqrt{\frac{x - 1}{\sqrt{x - 2} \left(x + 2\right)}} \left(\frac{x^{3} \left(4 \sqrt{x - 2} \left(\frac{3 \left(2 - \frac{x + 2}{x - 2}\right) \left(x - 1\right)}{\left(x - 2\right)^{\frac{5}{2}} \left(x + 2\right)} + \frac{8 \left(4 - \frac{x + 2}{x - 2}\right) \left(x - 1\right)}{\left(x - 2\right)^{\frac{3}{2}} \left(x + 2\right)^{2}} - \frac{4 \left(4 - \frac{x + 2}{x - 2}\right)}{\left(x - 2\right)^{\frac{3}{2}} \left(x + 2\right)} + \frac{4 \left(4 - \frac{x + 2}{x - 2}\right) \left(x - 1\right)}{\left(x - 2\right)^{\frac{5}{2}} \left(x + 2\right)} - \frac{24 \left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)^{3}} + \frac{16 \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)^{2}} - \frac{16 \left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right)^{2} \left(x + 2\right)^{2}} + \frac{8 \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right)^{2} \left(x + 2\right)} - \frac{8 \left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right)^{3} \left(x + 2\right)} + \frac{16}{\sqrt{x - 2} \left(x + 2\right)^{2}} + \frac{8}{\left(x - 2\right)^{\frac{3}{2}} \left(x + 2\right)} + \frac{6}{\left(x - 2\right)^{\frac{5}{2}}}\right) - \frac{16 \sqrt{x - 2} \left(\frac{\left(4 - \frac{x + 2}{x - 2}\right) \left(x - 1\right)}{\left(x - 2\right)^{\frac{3}{2}} \left(x + 2\right)} - \frac{4 \left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)^{2}} + \frac{2 \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2 \left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right)^{2} \left(x + 2\right)} + \frac{4}{\sqrt{x - 2} \left(x + 2\right)} + \frac{2}{\left(x - 2\right)^{\frac{3}{2}}}\right)}{x + 2} + \frac{2 \sqrt{x - 2} \left(\left(x - 1\right) \left(\frac{2}{x + 2} + \frac{1}{x - 2}\right) - 2\right) \left(\frac{\left(4 - \frac{x + 2}{x - 2}\right) \left(x - 1\right)}{\left(x - 2\right)^{\frac{3}{2}} \left(x + 2\right)} - \frac{4 \left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)^{2}} + \frac{2 \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2 \left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right)^{2} \left(x + 2\right)} + \frac{4}{\sqrt{x - 2} \left(x + 2\right)} + \frac{2}{\left(x - 2\right)^{\frac{3}{2}}}\right)}{x - 1} + \frac{2 \sqrt{x - 2} \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right) \left(- \left(x - 1\right) \left(\frac{8}{\left(x + 2\right)^{2}} + \frac{4}{\left(x - 2\right) \left(x + 2\right)} + \frac{3}{\left(x - 2\right)^{2}}\right) + \frac{8}{x + 2} + \frac{4}{x - 2}\right)}{x - 1} + \frac{2 \sqrt{x - 2} \left(\frac{2 \left(x - 1\right)}{x + 2} - 2 + \frac{x - 1}{x - 2}\right) \left(\frac{\left(4 - \frac{x + 2}{x - 2}\right) \left(x - 1\right)}{\left(x - 2\right)^{\frac{3}{2}} \left(x + 2\right)} - \frac{4 \left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)^{2}} + \frac{2 \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2 \left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right)^{2} \left(x + 2\right)} + \frac{4}{\sqrt{x - 2} \left(x + 2\right)} + \frac{2}{\left(x - 2\right)^{\frac{3}{2}}}\right)}{x - 1} + \frac{16 \sqrt{x - 2} \left(\frac{\left(4 - \frac{x + 2}{x - 2}\right) \left(x - 1\right)}{\left(x - 2\right)^{\frac{3}{2}} \left(x + 2\right)} - \frac{4 \left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)^{2}} + \frac{2 \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2 \left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right)^{2} \left(x + 2\right)} + \frac{4}{\sqrt{x - 2} \left(x + 2\right)} + \frac{2}{\left(x - 2\right)^{\frac{3}{2}}}\right)}{x - 1} + \frac{8 \sqrt{x - 2} \left(\left(x - 1\right) \left(\frac{2}{x + 2} + \frac{1}{x - 2}\right) - 2\right) \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right)}{\left(x - 1\right) \left(x + 2\right)} + \frac{4 \sqrt{x - 2} \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right) \left(\frac{2 \left(x - 1\right)}{x + 2} - 2 + \frac{x - 1}{x - 2}\right)}{\left(x - 1\right) \left(x + 2\right)} + \frac{32 \sqrt{x - 2} \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right)}{\left(x - 1\right) \left(x + 2\right)} - \frac{\sqrt{x - 2} \left(\left(x - 1\right) \left(\frac{2}{x + 2} + \frac{1}{x - 2}\right) - 2\right) \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right) \left(\frac{2 \left(x - 1\right)}{x + 2} - 2 + \frac{x - 1}{x - 2}\right)}{\left(x - 1\right)^{2}} - \frac{8 \sqrt{x - 2} \left(\left(x - 1\right) \left(\frac{2}{x + 2} + \frac{1}{x - 2}\right) - 2\right) \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right)}{\left(x - 1\right)^{2}} - \frac{4 \sqrt{x - 2} \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right) \left(\frac{2 \left(x - 1\right)}{x + 2} - 2 + \frac{x - 1}{x - 2}\right)}{\left(x - 1\right)^{2}} - \frac{32 \sqrt{x - 2} \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right)}{\left(x - 1\right)^{2}} - \frac{8 \left(\frac{\left(4 - \frac{x + 2}{x - 2}\right) \left(x - 1\right)}{\left(x - 2\right)^{\frac{3}{2}} \left(x + 2\right)} - \frac{4 \left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)^{2}} + \frac{2 \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2 \left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right)^{2} \left(x + 2\right)} + \frac{4}{\sqrt{x - 2} \left(x + 2\right)} + \frac{2}{\left(x - 2\right)^{\frac{3}{2}}}\right)}{\sqrt{x - 2}} - \frac{16 \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right)}{\sqrt{x - 2} \left(x + 2\right)} + \frac{4 \left(\left(x - 1\right) \left(\frac{2}{x + 2} + \frac{1}{x - 2}\right) - 2\right) \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right)}{\sqrt{x - 2} \left(x - 1\right)} + \frac{2 \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right) \left(\frac{2 \left(x - 1\right)}{x + 2} - 2 + \frac{x - 1}{x - 2}\right)}{\sqrt{x - 2} \left(x - 1\right)} + \frac{16 \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right)}{\sqrt{x - 2} \left(x - 1\right)} + \frac{4 \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right)}{\left(x - 2\right)^{\frac{3}{2}}}\right)}{64 \left(x - 1\right)} - \frac{9 x^{2} \left(2 \sqrt{x - 2} \left(\frac{\left(4 - \frac{x + 2}{x - 2}\right) \left(x - 1\right)}{\left(x - 2\right)^{\frac{3}{2}} \left(x + 2\right)} - \frac{4 \left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)^{2}} + \frac{2 \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2 \left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right)^{2} \left(x + 2\right)} + \frac{4}{\sqrt{x - 2} \left(x + 2\right)} + \frac{2}{\left(x - 2\right)^{\frac{3}{2}}}\right) + \frac{4 \sqrt{x - 2} \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right)}{x + 2} - \frac{\sqrt{x - 2} \left(\left(x - 1\right) \left(\frac{2}{x + 2} + \frac{1}{x - 2}\right) - 2\right) \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right)}{x - 1} - \frac{4 \sqrt{x - 2} \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right)}{x - 1} + \frac{2 \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right)}{\sqrt{x - 2}}\right)}{16 \left(x - 1\right)} - \frac{9 x \sqrt{x - 2} \left(\frac{\left(x - 1\right) \left(2 \sqrt{x - 2} + \frac{x + 2}{\sqrt{x - 2}}\right)}{\left(x - 2\right) \left(x + 2\right)} - \frac{2}{\sqrt{x - 2}}\right)}{2 \left(x - 1\right)} + 6\right)$$

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Gráfico

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

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

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Solución

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

Gráfico:

Definida a trozos:

Solución

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