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Derivada de:
Derivada de x^4/3-x
Derivada de x^-4/5
Derivada de x=1
Derivada de x^2*2^x
Expresiones idénticas
y=sqrt((x*(x- uno)*(x- dos))/(x- tres))
y es igual a raíz cuadrada de ((x multiplicar por (x menos 1) multiplicar por (x menos 2)) dividir por (x menos 3))
y es igual a raíz cuadrada de ((x multiplicar por (x menos uno) multiplicar por (x menos dos)) dividir por (x menos tres))
y=√((x*(x-1)*(x-2))/(x-3))
y=sqrt((x(x-1)(x-2))/(x-3))
y=sqrtxx-1x-2/x-3
y=sqrt((x*(x-1)*(x-2)) dividir por (x-3))
Expresiones semejantes
y=sqrt((x*(x-1)*(x-2))/(x+3))
y=sqrt((x*(x+1)*(x-2))/(x-3))
y=sqrt((x*(x-1)*(x+2))/(x-3))

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

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

Solución

Ha introducido [src]

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

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

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

Solución detallada

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

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

$\frac{x^{3} - 6 x^{2} + 9 x - 3}{\sqrt{\frac{x \left(x^{2} - 3 x + 2\right)}{x - 3}} \left(x^{2} - 6 x + 9\right)}$

Respuesta:

$\frac{x^{3} - 6 x^{2} + 9 x - 3}{\sqrt{\frac{x \left(x^{2} - 3 x + 2\right)}{x - 3}} \left(x^{2} - 6 x + 9\right)}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

                          /                                               x*(-1 + x)*(-2 + x)                                       x*(-1 + x)*(-2 + x)                                       x*(-1 + x)*(-2 + x)                                                                          x*(-1 + x)*(-2 + x)                                                                       /                                    x*(-1 + x)*(-2 + x)\ /                                              x*(-1 + x)*(-2 + x)\\
    _____________________ |           -x*(-1 + x) - (-1 + 2*x)*(-2 + x) + -------------------   -x*(-1 + x) - (-1 + 2*x)*(-2 + x) + -------------------   -x*(-1 + x) - (-1 + 2*x)*(-2 + x) + -------------------                                      -x*(-1 + x) - (-1 + 2*x)*(-2 + x) + -------------------                                                                       |-x*(-1 + x) - (-1 + 2*x)*(-2 + x) + -------------------|*|x*(-1 + x) + x*(-2 + x) + (-1 + x)*(-2 + x) - -------------------||
   / x*(-1 + x)*(-2 + x)  |                                                      -3 + x                                                    -3 + x                                                    -3 + x         x*(-1 + x) + (-1 + 2*x)*(-2 + x)                                              -3 + x         x*(-1 + x)   x*(-2 + x)   (-1 + x)*(-2 + x)   x*(-1 + x)*(-2 + x)   \                                           -3 + x      / \                                                     -3 + x      /|
  /  ------------------- *|-3 + 3*x + ------------------------------------------------------- + ------------------------------------------------------- + ------------------------------------------------------- - -------------------------------- - ------------------------------------------------------- - ---------- - ---------- - ----------------- + ------------------- - -----------------------------------------------------------------------------------------------------------------------------|
\/          -3 + x        |                                     2*x                                                    2*(-1 + x)                                                2*(-2 + x)                                    2*(-3 + x)                                     2*(-3 + x)                         2*(-3 + x)   2*(-3 + x)       2*(-3 + x)                   2                                                            4*x*(-1 + x)*(-2 + x)                                                    |
                          \                                                                                                                                                                                                                                                                                                                                         (-3 + x)                                                                                                                                      /
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                                                                                                                                                                                                                                                x*(-1 + x)*(-2 + x)

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

Simplificar

Tercera derivada [src]

                          /              x*(-1 + x) + (-1 + 2*x)*(-2 + x)   x*(-1 + x)   x*(-2 + x)   (-1 + x)*(-2 + x)   2*x*(-1 + x)*(-2 + x)             x*(-1 + x) + (-1 + 2*x)*(-2 + x)   x*(-1 + x)   x*(-2 + x)   (-1 + x)*(-2 + x)   2*x*(-1 + x)*(-2 + x)                                                x*(-1 + x) + (-1 + 2*x)*(-2 + x)   x*(-1 + x)   x*(-2 + x)   (-1 + x)*(-2 + x)   2*x*(-1 + x)*(-2 + x)                                                                                                                                                   x*(-1 + x) + (-1 + 2*x)*(-2 + x)   x*(-1 + x)   x*(-2 + x)   (-1 + x)*(-2 + x)   2*x*(-1 + x)*(-2 + x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  /                                    x*(-1 + x)*(-2 + x)\ /           x*(-1 + x)   x*(-2 + x)   (-1 + x)*(-2 + x)   x*(-1 + x)*(-2 + x)\   /                                              x*(-1 + x)*(-2 + x)\ /          x*(-1 + x) + (-1 + 2*x)*(-2 + x)   x*(-1 + x)   x*(-2 + x)   (-1 + x)*(-2 + x)   2*x*(-1 + x)*(-2 + x)\                                                                      2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  \
                          |    6 - 6*x + -------------------------------- + ---------- + ---------- + ----------------- - ---------------------   6 - 6*x + -------------------------------- + ---------- + ---------- + ----------------- - ---------------------                                      6 - 6*x + -------------------------------- + ---------- + ---------- + ----------------- - ---------------------                                                x*(-1 + x)*(-2 + x)                                       x*(-1 + x)*(-2 + x)            6 - 6*x + -------------------------------- + ---------- + ---------- + ----------------- - ---------------------                                       x*(-1 + x)*(-2 + x)                                                    x*(-1 + x)*(-2 + x)                                       x*(-1 + x)*(-2 + x)                                       x*(-1 + x)*(-2 + x)                                       x*(-1 + x)*(-2 + x)                                       x*(-1 + x)*(-2 + x)                                       x*(-1 + x)*(-2 + x)                                                                               |-x*(-1 + x) - (-1 + 2*x)*(-2 + x) + -------------------|*|-3 + 3*x - ---------- - ---------- - ----------------- + -------------------|   |x*(-1 + x) + x*(-2 + x) + (-1 + x)*(-2 + x) - -------------------|*|6 - 6*x + -------------------------------- + ---------- + ---------- + ----------------- - ---------------------|   /                                              x*(-1 + x)*(-2 + x)\  /                                    x*(-1 + x)*(-2 + x)\     /                                    x*(-1 + x)*(-2 + x)\ /                                              x*(-1 + x)*(-2 + x)\     /                                    x*(-1 + x)*(-2 + x)\ /                                              x*(-1 + x)*(-2 + x)\     /                                    x*(-1 + x)*(-2 + x)\ /                                              x*(-1 + x)*(-2 + x)\     /                                    x*(-1 + x)*(-2 + x)\ /                                              x*(-1 + x)*(-2 + x)\|
    _____________________ |                           -3 + x                  -3 + x       -3 + x           -3 + x                      2                                -3 + x                  -3 + x       -3 + x           -3 + x                      2                                                                   -3 + x                  -3 + x       -3 + x           -3 + x                      2                  -x*(-1 + x) - (-1 + 2*x)*(-2 + x) + -------------------   -x*(-1 + x) - (-1 + 2*x)*(-2 + x) + -------------------                                   -3 + x                  -3 + x       -3 + x           -3 + x                      2         -x*(-1 + x) - (-1 + 2*x)*(-2 + x) + -------------------                -x*(-1 + x) - (-1 + 2*x)*(-2 + x) + -------------------   -x*(-1 + x) - (-1 + 2*x)*(-2 + x) + -------------------   -x*(-1 + x) - (-1 + 2*x)*(-2 + x) + -------------------   -x*(-1 + x) - (-1 + 2*x)*(-2 + x) + -------------------   -x*(-1 + x) - (-1 + 2*x)*(-2 + x) + -------------------   -x*(-1 + x) - (-1 + 2*x)*(-2 + x) + -------------------                                                                               \                                           -3 + x      / |             -3 + x       -3 + x           -3 + x                     2     |   \                                                     -3 + x      / |                       -3 + x                  -3 + x       -3 + x           -3 + x                      2      |   |x*(-1 + x) + x*(-2 + x) + (-1 + x)*(-2 + x) - -------------------| *|-x*(-1 + x) - (-1 + 2*x)*(-2 + x) + -------------------|   3*|-x*(-1 + x) - (-1 + 2*x)*(-2 + x) + -------------------|*|x*(-1 + x) + x*(-2 + x) + (-1 + x)*(-2 + x) - -------------------|   3*|-x*(-1 + x) - (-1 + 2*x)*(-2 + x) + -------------------|*|x*(-1 + x) + x*(-2 + x) + (-1 + x)*(-2 + x) - -------------------|   3*|-x*(-1 + x) - (-1 + 2*x)*(-2 + x) + -------------------|*|x*(-1 + x) + x*(-2 + x) + (-1 + x)*(-2 + x) - -------------------|   3*|-x*(-1 + x) - (-1 + 2*x)*(-2 + x) + -------------------|*|x*(-1 + x) + x*(-2 + x) + (-1 + x)*(-2 + x) - -------------------||
   / x*(-1 + x)*(-2 + x)  |                                                                                                     (-3 + x)                                                                                                           (-3 + x)          x*(-1 + x) + (-1 + 2*x)*(-2 + x)                                                                                                    (-3 + x)            x                                                 -3 + x                                                    -3 + x         -2 + x                                                                                                    (-3 + x)                                                     -3 + x         7*(-1 + x)                                              -3 + x                                                    -3 + x                                                    -3 + x                                                    -3 + x                                                    -3 + x                                                    -3 + x         2*x*(-1 + x)   2*x*(-2 + x)   2*(-1 + x)*(-2 + x)   3*x*(-1 + x)*(-2 + x)                                                             \                                                              (-3 + x)      /                                                                       \                                                                                                 (-3 + x)       /   \                                                     -3 + x      /  \                                           -3 + x      /     \                                           -3 + x      / \                                                     -3 + x      /     \                                           -3 + x      / \                                                     -3 + x      /     \                                           -3 + x      / \                                                     -3 + x      /     \                                           -3 + x      / \                                                     -3 + x      /|
  /  ------------------- *|3 + ---------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------- + -------------------------------- + ---------------------------------------------------------------------------------------------------------------- - ------ - ------------------------------------------------------- - ------------------------------------------------------- - ------ - ---------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------- - ---------- + ------------------------------------------------------- + ------------------------------------------------------- + ------------------------------------------------------- - ------------------------------------------------------- - ------------------------------------------------------- - ------------------------------------------------------- + ------------ + ------------ + ------------------- - --------------------- - ---------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------|
\/          -3 + x        |                                                           x                                                                                                                -1 + x                                                                           2                                                                    -2 + x                                                        -3 + x                               2                                                            2                          -3 + x                                                        -3 + x                                                                                       2                            -3 + x                            x*(-3 + x)                                            (-1 + x)*(-3 + x)                                         (-3 + x)*(-2 + x)                                             x*(-1 + x)                                                x*(-2 + x)                                            (-1 + x)*(-2 + x)                               2              2                  2                      3                                                                  2*x*(-1 + x)*(-2 + x)                                                                                                                                             2*x*(-1 + x)*(-2 + x)                                                                                                                                          2         2         2                                                                                                                                2                                                                                                                        2                                                                                                                        2                                                                                                                          4*x*(-1 + x)*(-3 + x)*(-2 + x)                                                |
                          \                                                                                                                                                                                                                                                     (-3 + x)                                                                                                                                                                       x                                                     (-1 + x)                                                                                                                                                                              (-2 + x)                                                                                                                                                                                                                                                                                                                                                                                                     (-3 + x)       (-3 + x)           (-3 + x)               (-3 + x)                                                                                                                                                                                                                                                                                                                                                                                                 8*x *(-1 + x) *(-2 + x)                                                                                                            4*x*(-1 + x)*(-2 + x)                                                                                                             4*x*(-1 + x) *(-2 + x)                                                                                                            4*x *(-1 + x)*(-2 + x)                                                                                                                                                                                      /
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             x*(-1 + x)*(-2 + x)

$$\frac{\sqrt{\frac{x \left(x - 2\right) \left(x - 1\right)}{x - 3}} \left(- \frac{x}{x - 3} + \frac{2 x \left(x - 2\right)}{\left(x - 3\right)^{2}} + \frac{2 x \left(x - 1\right)}{\left(x - 3\right)^{2}} - \frac{3 x \left(x - 2\right) \left(x - 1\right)}{\left(x - 3\right)^{3}} + 3 + \frac{- 6 x + \frac{x \left(x - 2\right)}{x - 3} + \frac{x \left(x - 1\right)}{x - 3} - \frac{2 x \left(x - 2\right) \left(x - 1\right)}{\left(x - 3\right)^{2}} + 6 + \frac{\left(x - 2\right) \left(x - 1\right)}{x - 3} + \frac{x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)}{x - 3}}{x - 1} - \frac{- x \left(x - 1\right) + \frac{x \left(x - 2\right) \left(x - 1\right)}{x - 3} - \left(x - 2\right) \left(2 x - 1\right)}{\left(x - 1\right)^{2}} + \frac{- 6 x + \frac{x \left(x - 2\right)}{x - 3} + \frac{x \left(x - 1\right)}{x - 3} - \frac{2 x \left(x - 2\right) \left(x - 1\right)}{\left(x - 3\right)^{2}} + 6 + \frac{\left(x - 2\right) \left(x - 1\right)}{x - 3} + \frac{x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)}{x - 3}}{x - 2} - \frac{- x \left(x - 1\right) + \frac{x \left(x - 2\right) \left(x - 1\right)}{x - 3} - \left(x - 2\right) \left(2 x - 1\right)}{\left(x - 2\right) \left(x - 1\right)} - \frac{- x \left(x - 1\right) + \frac{x \left(x - 2\right) \left(x - 1\right)}{x - 3} - \left(x - 2\right) \left(2 x - 1\right)}{\left(x - 2\right)^{2}} - \frac{x - 2}{x - 3} - \frac{7 \left(x - 1\right)}{x - 3} - \frac{- 6 x + \frac{x \left(x - 2\right)}{x - 3} + \frac{x \left(x - 1\right)}{x - 3} - \frac{2 x \left(x - 2\right) \left(x - 1\right)}{\left(x - 3\right)^{2}} + 6 + \frac{\left(x - 2\right) \left(x - 1\right)}{x - 3} + \frac{x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)}{x - 3}}{x - 3} + \frac{- x \left(x - 1\right) + \frac{x \left(x - 2\right) \left(x - 1\right)}{x - 3} - \left(x - 2\right) \left(2 x - 1\right)}{\left(x - 3\right) \left(x - 1\right)} + \frac{- x \left(x - 1\right) + \frac{x \left(x - 2\right) \left(x - 1\right)}{x - 3} - \left(x - 2\right) \left(2 x - 1\right)}{\left(x - 3\right) \left(x - 2\right)} + \frac{2 \left(x - 2\right) \left(x - 1\right)}{\left(x - 3\right)^{2}} + \frac{x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)}{\left(x - 3\right)^{2}} + \frac{- 6 x + \frac{x \left(x - 2\right)}{x - 3} + \frac{x \left(x - 1\right)}{x - 3} - \frac{2 x \left(x - 2\right) \left(x - 1\right)}{\left(x - 3\right)^{2}} + 6 + \frac{\left(x - 2\right) \left(x - 1\right)}{x - 3} + \frac{x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)}{x - 3}}{x} - \frac{- x \left(x - 1\right) + \frac{x \left(x - 2\right) \left(x - 1\right)}{x - 3} - \left(x - 2\right) \left(2 x - 1\right)}{x \left(x - 1\right)} - \frac{- x \left(x - 1\right) + \frac{x \left(x - 2\right) \left(x - 1\right)}{x - 3} - \left(x - 2\right) \left(2 x - 1\right)}{x \left(x - 2\right)} - \frac{\left(- x \left(x - 1\right) + \frac{x \left(x - 2\right) \left(x - 1\right)}{x - 3} - \left(x - 2\right) \left(2 x - 1\right)\right) \left(3 x - \frac{x \left(x - 2\right)}{x - 3} - \frac{x \left(x - 1\right)}{x - 3} + \frac{x \left(x - 2\right) \left(x - 1\right)}{\left(x - 3\right)^{2}} - 3 - \frac{\left(x - 2\right) \left(x - 1\right)}{x - 3}\right)}{2 x \left(x - 2\right) \left(x - 1\right)} - \frac{\left(x \left(x - 2\right) + x \left(x - 1\right) - \frac{x \left(x - 2\right) \left(x - 1\right)}{x - 3} + \left(x - 2\right) \left(x - 1\right)\right) \left(- 6 x + \frac{x \left(x - 2\right)}{x - 3} + \frac{x \left(x - 1\right)}{x - 3} - \frac{2 x \left(x - 2\right) \left(x - 1\right)}{\left(x - 3\right)^{2}} + 6 + \frac{\left(x - 2\right) \left(x - 1\right)}{x - 3} + \frac{x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)}{x - 3}\right)}{2 x \left(x - 2\right) \left(x - 1\right)} + \frac{3 \left(- x \left(x - 1\right) + \frac{x \left(x - 2\right) \left(x - 1\right)}{x - 3} - \left(x - 2\right) \left(2 x - 1\right)\right) \left(x \left(x - 2\right) + x \left(x - 1\right) - \frac{x \left(x - 2\right) \left(x - 1\right)}{x - 3} + \left(x - 2\right) \left(x - 1\right)\right)}{4 x \left(x - 2\right) \left(x - 1\right)^{2}} + \frac{3 \left(- x \left(x - 1\right) + \frac{x \left(x - 2\right) \left(x - 1\right)}{x - 3} - \left(x - 2\right) \left(2 x - 1\right)\right) \left(x \left(x - 2\right) + x \left(x - 1\right) - \frac{x \left(x - 2\right) \left(x - 1\right)}{x - 3} + \left(x - 2\right) \left(x - 1\right)\right)}{4 x \left(x - 2\right)^{2} \left(x - 1\right)} + \frac{- x \left(x - 1\right) + \frac{x \left(x - 2\right) \left(x - 1\right)}{x - 3} - \left(x - 2\right) \left(2 x - 1\right)}{x \left(x - 3\right)} - \frac{3 \left(- x \left(x - 1\right) + \frac{x \left(x - 2\right) \left(x - 1\right)}{x - 3} - \left(x - 2\right) \left(2 x - 1\right)\right) \left(x \left(x - 2\right) + x \left(x - 1\right) - \frac{x \left(x - 2\right) \left(x - 1\right)}{x - 3} + \left(x - 2\right) \left(x - 1\right)\right)}{4 x \left(x - 3\right) \left(x - 2\right) \left(x - 1\right)} - \frac{- x \left(x - 1\right) + \frac{x \left(x - 2\right) \left(x - 1\right)}{x - 3} - \left(x - 2\right) \left(2 x - 1\right)}{x^{2}} + \frac{3 \left(- x \left(x - 1\right) + \frac{x \left(x - 2\right) \left(x - 1\right)}{x - 3} - \left(x - 2\right) \left(2 x - 1\right)\right) \left(x \left(x - 2\right) + x \left(x - 1\right) - \frac{x \left(x - 2\right) \left(x - 1\right)}{x - 3} + \left(x - 2\right) \left(x - 1\right)\right)}{4 x^{2} \left(x - 2\right) \left(x - 1\right)} - \frac{\left(- x \left(x - 1\right) + \frac{x \left(x - 2\right) \left(x - 1\right)}{x - 3} - \left(x - 2\right) \left(2 x - 1\right)\right) \left(x \left(x - 2\right) + x \left(x - 1\right) - \frac{x \left(x - 2\right) \left(x - 1\right)}{x - 3} + \left(x - 2\right) \left(x - 1\right)\right)^{2}}{8 x^{2} \left(x - 2\right)^{2} \left(x - 1\right)^{2}}\right)}{x \left(x - 2\right) \left(x - 1\right)}$$

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Gráfico

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

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

Gráfico:

Definida a trozos:

Solución

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

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

Gráfico:

Definida a trozos:

Solución

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