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Derivada de:
Derivada de 1/(x+3)
Derivada de 4*y
Derivada de (-1)/x-3*x
Derivada de y=csc(3x²+1)
Expresiones idénticas
y=sqrt((tres x- cinco)^ cuatro (2x^3+ nueve)/(4x+ siete))
y es igual a raíz cuadrada de ((3x menos 5) en el grado 4(2x al cubo más 9) dividir por (4x más 7))
y es igual a raíz cuadrada de ((tres x menos cinco) en el grado cuatro (2x al cubo más nueve) dividir por (4x más siete))
y=√((3x-5)^4(2x^3+9)/(4x+7))
y=sqrt((3x-5)4(2x3+9)/(4x+7))
y=sqrt3x-542x3+9/4x+7
y=sqrt((3x-5)⁴(2x³+9)/(4x+7))
y=sqrt((3x-5) en el grado 4(2x en el grado 3+9)/(4x+7))
y=sqrt3x-5^42x^3+9/4x+7
y=sqrt((3x-5)^4(2x^3+9) dividir por (4x+7))
Expresiones semejantes
y=sqrt((3x-5)^4(2x^3-9)/(4x+7))
y=sqrt((3x-5)^4(2x^3+9)/(4x-7))
y=sqrt((3x+5)^4(2x^3+9)/(4x+7))

Derivada de la función/ y=sqrt((3x-5)^4(2x^3+9)/(4x+7))

Derivada de y=sqrt((3x-5)^4(2x^3+9)/(4x+7))

Solución

Ha introducido [src]

     _______________________
    /          4 /   3    \ 
   /  (3*x - 5) *\2*x  + 9/ 
  /   --------------------- 
\/           4*x + 7

$$\sqrt{\frac{\left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)}{4 x + 7}}$$

sqrt(((3*x - 5)^4*(2*x^3 + 9))/(4*x + 7))

Solución detallada

Sustituimos $u = \frac{\left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)}{4 x + 7}$ .
Según el principio, aplicamos: $\sqrt{u}$ tenemos $\frac{1}{2 \sqrt{u}}$
Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \frac{\left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)}{4 x + 7}$ :
1. Se aplica la regla de la derivada parcial:
  
  $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
  
  $f{\left(x \right)} = \left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)$ y $g{\left(x \right)} = 4 x + 7$ .
  
  Para calcular $\frac{d}{d x} f{\left(x \right)}$ :
  1. Se aplica la regla de la derivada de una multiplicación:
    
    $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
    
    $f{\left(x \right)} = \left(3 x - 5\right)^{4}$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
    1. Sustituimos $u = 3 x - 5$ .
    2. Según el principio, aplicamos: $u^{4}$ tenemos $4 u^{3}$
    3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \left(3 x - 5\right)$ :
      1. diferenciamos $3 x - 5$ miembro por miembro:
        
        La derivada de una constante $-5$ es igual a cero.
        
        La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
        
        Según el principio, aplicamos: $x$ tenemos $1$
        
        Entonces, como resultado: $3$
        
        Como resultado de: $3$
      Como resultado de la secuencia de reglas:
      
      $12 \left(3 x - 5\right)^{3}$
    $g{\left(x \right)} = 2 x^{3} + 9$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
    1. diferenciamos $2 x^{3} + 9$ miembro por miembro:
      1. La derivada de una constante $9$ es igual a cero.
      2. La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
        
        Según el principio, aplicamos: $x^{3}$ tenemos $3 x^{2}$
        
        Entonces, como resultado: $6 x^{2}$
      Como resultado de: $6 x^{2}$
    Como resultado de: $6 x^{2} \left(3 x - 5\right)^{4} + 12 \left(3 x - 5\right)^{3} \left(2 x^{3} + 9\right)$
  Para calcular $\frac{d}{d x} g{\left(x \right)}$ :
  1. diferenciamos $4 x + 7$ miembro por miembro:
    1. La derivada de una constante $7$ es igual a cero.
    2. La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
      1. Según el principio, aplicamos: $x$ tenemos $1$
      Entonces, como resultado: $4$
    Como resultado de: $4$
  Ahora aplicamos la regla de la derivada de una divesión:
  
  $\frac{- 4 \left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right) + \left(4 x + 7\right) \left(6 x^{2} \left(3 x - 5\right)^{4} + 12 \left(3 x - 5\right)^{3} \left(2 x^{3} + 9\right)\right)}{\left(4 x + 7\right)^{2}}$
Como resultado de la secuencia de reglas:

$\frac{- 4 \left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right) + \left(4 x + 7\right) \left(6 x^{2} \left(3 x - 5\right)^{4} + 12 \left(3 x - 5\right)^{3} \left(2 x^{3} + 9\right)\right)}{2 \sqrt{\frac{2 x^{3} + 9}{4 x + 7}} \left(3 x - 5\right)^{2} \left(4 x + 7\right)^{2}}$
Simplificamos:

$\frac{216 x^{5} - 39 x^{4} - 850 x^{3} + 1011 x^{2} + 594 x - 2340}{\sqrt{\frac{2 x^{3} + 9}{4 x + 7}} \left(16 x^{2} + 56 x + 49\right)}$

Respuesta:

$\frac{216 x^{5} - 39 x^{4} - 850 x^{3} + 1011 x^{2} + 594 x - 2340}{\sqrt{\frac{2 x^{3} + 9}{4 x + 7}} \left(16 x^{2} + 56 x + 49\right)}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

     _______________________                                                                                 
    /          4 /   3    \            /   2          4               3 /   3    \              4 /   3    \\
   /  (3*x - 5) *\2*x  + 9/            |6*x *(3*x - 5)  + 12*(3*x - 5) *\2*x  + 9/   2*(3*x - 5) *\2*x  + 9/|
  /   --------------------- *(4*x + 7)*|------------------------------------------ - -----------------------|
\/           4*x + 7                   |               2*(4*x + 7)                                   2      |
                                       \                                                    (4*x + 7)       /
-------------------------------------------------------------------------------------------------------------
                                            /   3    \          4                                            
                                            \2*x  + 9/*(3*x - 5)

$$\frac{\sqrt{\frac{\left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)}{4 x + 7}} \left(4 x + 7\right) \left(- \frac{2 \left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} + \frac{6 x^{2} \left(3 x - 5\right)^{4} + 12 \left(3 x - 5\right)^{3} \left(2 x^{3} + 9\right)}{2 \left(4 x + 7\right)}\right)}{\left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)}$$

Simplificar

Segunda derivada [src]

                /                                                    /                                             /       3\\ /                                            /       3\\                                                                                /                                             /       3\\                                               /                                             /       3\\\
     __________ |                                                    |          3      2              2*(-5 + 3*x)*\9 + 2*x /| |         3      2              2*(-5 + 3*x)*\9 + 2*x /|                                                                                |          3      2              2*(-5 + 3*x)*\9 + 2*x /|                                  2            |          3      2              2*(-5 + 3*x)*\9 + 2*x /||
    /        3  |                                                    |-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|       2           2                 /        3    2           \   4*(-5 + 3*x)*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|                2 /       3\   6*x *(-5 + 3*x)*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------||
   /  9 + 2*x   |           3                 2       2              \                                        7 + 4*x        / \                                       7 + 4*x        /   12*x *(-5 + 3*x)    12*(-5 + 3*x)*\18 + 4*x  + x *(-5 + 3*x)/                \                                        7 + 4*x        /   16*(-5 + 3*x) *\9 + 2*x /                   \                                        7 + 4*x        /|
  /   -------- *|-162 - 36*x  + 6*x*(-5 + 3*x)  + 36*x *(-5 + 3*x) - ------------------------------------------------------------------------------------------------------------------ - ----------------- - ----------------------------------------- - ---------------------------------------------------------------------- + ------------------------- + -------------------------------------------------------------------------|
\/    7 + 4*x   |                                                                                                                3                                                             7 + 4*x                         7 + 4*x                                                   7 + 4*x                                                    2                                                  3                                |
                \                                                                                                         9 + 2*x                                                                                                                                                                                                          (7 + 4*x)                                            9 + 2*x                                 /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                        3                                                                                                                                                                                                                
                                                                                                                                                                                                                 9 + 2*x

$$\frac{\sqrt{\frac{2 x^{3} + 9}{4 x + 7}} \left(- 36 x^{3} - \frac{12 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} + 36 x^{2} \left(3 x - 5\right) + \frac{6 x^{2} \left(3 x - 5\right) \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{2 x^{3} + 9} + 6 x \left(3 x - 5\right)^{2} + \frac{16 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} - \frac{12 \left(3 x - 5\right) \left(4 x^{3} + x^{2} \left(3 x - 5\right) + 18\right)}{4 x + 7} - \frac{4 \left(3 x - 5\right) \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{4 x + 7} - 162 - \frac{\left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right) \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)}{2 x^{3} + 9}\right)}{2 x^{3} + 9}$$

Simplificar

Tercera derivada [src]

                /                                                                     /                                                                2 /       3\      2           2                /        3    2           \                 /       3\\     /                                                                                  2 /       3\       2           3                2 /        3    2           \                 3                /         3               2       2           \                3 /       3\                 /       3\       2           2\      /                                                                2 /       3\      2           2                /        3    2           \                 /       3\\                                                                                                                                       /         /       3\\ /                                                                2 /       3\      2           2                /        3    2           \                 /       3\\                                                                                              /                                                                2 /       3\      2           2                /        3    2           \                 /       3\\                                                                                                                                                                                                                                                                                                                                                    /                                             /       3\\ /                                                                 /       3\       2           2               2 /       3\\     /                                            /       3\\ /                                                                2 /       3\      2           2                /        3    2           \                 /       3\\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \
                |      /                                             /       3\\      |           3       2                            2   8*(-5 + 3*x) *\9 + 2*x /   6*x *(-5 + 3*x)    6*(-5 + 3*x)*\18 + 4*x  + x *(-5 + 3*x)/   12*(-5 + 3*x)*\9 + 2*x /|     |                 3        3        2                             2   64*(-5 + 3*x) *\9 + 2*x /   32*x *(-5 + 3*x)    16*(-5 + 3*x) *\18 + 4*x  + x *(-5 + 3*x)/   4*x*(-5 + 3*x)    8*(-5 + 3*x)*\81 + 18*x  + x*(-5 + 3*x)  + 12*x *(-5 + 3*x)/   32*(-5 + 3*x) *\9 + 2*x /   36*(-5 + 3*x)*\9 + 2*x /   48*x *(-5 + 3*x) |      |           3       2                            2   8*(-5 + 3*x) *\9 + 2*x /   6*x *(-5 + 3*x)    6*(-5 + 3*x)*\18 + 4*x  + x *(-5 + 3*x)/   12*(-5 + 3*x)*\9 + 2*x /|      /                                             /       3\\          /                                             /       3\\     |   2   2*\9 + 2*x /| |           3       2                            2   8*(-5 + 3*x) *\9 + 2*x /   6*x *(-5 + 3*x)    6*(-5 + 3*x)*\18 + 4*x  + x *(-5 + 3*x)/   12*(-5 + 3*x)*\9 + 2*x /|      /         /       3\\ /                                             /       3\\       2 |           3       2                            2   8*(-5 + 3*x) *\9 + 2*x /   6*x *(-5 + 3*x)    6*(-5 + 3*x)*\18 + 4*x  + x *(-5 + 3*x)/   12*(-5 + 3*x)*\9 + 2*x /|   /         /       3\\ /                                             /       3\\ /                                            /       3\\                    /                                             /       3\\     /                                             /       3\\ /                                            /       3\\     |          3      2              2*(-5 + 3*x)*\9 + 2*x /| |          3                 2       2              24*(-5 + 3*x)*\9 + 2*x /   12*x *(-5 + 3*x)    8*(-5 + 3*x) *\9 + 2*x /|     |         3      2              2*(-5 + 3*x)*\9 + 2*x /| |           3       2                            2   8*(-5 + 3*x) *\9 + 2*x /   6*x *(-5 + 3*x)    6*(-5 + 3*x)*\18 + 4*x  + x *(-5 + 3*x)/   12*(-5 + 3*x)*\9 + 2*x /|                   /                                             /       3\\         /                                             /       3\\ /                                            /       3\\      /                                             /       3\\ /                                            /       3\\                /         /       3\\ /                                             /       3\\                   /         /       3\\ /                                             /       3\\                    /                                             /       3\\|
     __________ |      |          3      2              2*(-5 + 3*x)*\9 + 2*x /|   16*|-243 - 54*x  - 36*x *(-5 + 3*x) - 3*x*(-5 + 3*x)  - ------------------------ + ---------------- + ---------------------------------------- + ------------------------|   6*|-486 - (-5 + 3*x)  - 108*x  - 162*x *(-5 + 3*x) - 36*x*(-5 + 3*x)  - ------------------------- - ----------------- - ------------------------------------------ + --------------- + ------------------------------------------------------------ + ------------------------- + ------------------------ + -----------------|   36*|-243 - 54*x  - 36*x *(-5 + 3*x) - 3*x*(-5 + 3*x)  - ------------------------ + ---------------- + ---------------------------------------- + ------------------------|      |          3      2              2*(-5 + 3*x)*\9 + 2*x /|        2 |          3      2              2*(-5 + 3*x)*\9 + 2*x /|   2*|3*x  - ------------|*|-243 - 54*x  - 36*x *(-5 + 3*x) - 3*x*(-5 + 3*x)  - ------------------------ + ---------------- + ---------------------------------------- + ------------------------|      |   2   2*\9 + 2*x /| |          3      2              2*(-5 + 3*x)*\9 + 2*x /|   24*x *|-243 - 54*x  - 36*x *(-5 + 3*x) - 3*x*(-5 + 3*x)  - ------------------------ + ---------------- + ---------------------------------------- + ------------------------|   |   2   2*\9 + 2*x /| |          3      2              2*(-5 + 3*x)*\9 + 2*x /| |         3      2              2*(-5 + 3*x)*\9 + 2*x /|       4            |          3      2              2*(-5 + 3*x)*\9 + 2*x /|     |          3      2              2*(-5 + 3*x)*\9 + 2*x /| |         3      2              2*(-5 + 3*x)*\9 + 2*x /|   2*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|*|243 + 54*x  + 3*x*(-5 + 3*x)  + 36*x *(-5 + 3*x) - ------------------------ - ----------------- + ------------------------|   2*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|*|-243 - 54*x  - 36*x *(-5 + 3*x) - 3*x*(-5 + 3*x)  - ------------------------ + ---------------- + ---------------------------------------- + ------------------------|                   |          3      2              2*(-5 + 3*x)*\9 + 2*x /|       2 |          3      2              2*(-5 + 3*x)*\9 + 2*x /| |         3      2              2*(-5 + 3*x)*\9 + 2*x /|      |          3      2              2*(-5 + 3*x)*\9 + 2*x /| |         3      2              2*(-5 + 3*x)*\9 + 2*x /|                |   2   2*\9 + 2*x /| |          3      2              2*(-5 + 3*x)*\9 + 2*x /|      2            |   2   2*\9 + 2*x /| |          3      2              2*(-5 + 3*x)*\9 + 2*x /|       2            |          3      2              2*(-5 + 3*x)*\9 + 2*x /||
    /        3  |  108*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|      |                                                                    2              7 + 4*x                        7 + 4*x                            7 + 4*x         |     |                                                                                      2                       2                               2                       7 + 4*x                                 7 + 4*x                                               3                  7 + 4*x                 7 + 4*x     |      |                                                                    2              7 + 4*x                        7 + 4*x                            7 + 4*x         |   72*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|   108*x *|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|     \         7 + 4*x   / |                                                                    2              7 + 4*x                        7 + 4*x                            7 + 4*x         |   12*|3*x  - ------------|*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|         |                                                                    2              7 + 4*x                        7 + 4*x                            7 + 4*x         |   |3*x  - ------------|*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|   72*x *(-5 + 3*x)*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|   8*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|     \                                        7 + 4*x        / |                                                           7 + 4*x                 7 + 4*x                        2       |     \                                       7 + 4*x        / |                                                                    2              7 + 4*x                        7 + 4*x                            7 + 4*x         |   12*x*(-5 + 3*x)*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|   12*x *|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|   18*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|   4*(-5 + 3*x)*|3*x  - ------------|*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|   6*x *(-5 + 3*x)*|3*x  - ------------|*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|   48*x *(-5 + 3*x)*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------||
   /  9 + 2*x   |      \                                        7 + 4*x        /      \                                                           (7 + 4*x)                                                                                                 /     \                                                                             (7 + 4*x)               (7 + 4*x)                       (7 + 4*x)                                                                                                             (7 + 4*x)                                                       /      \                                                           (7 + 4*x)                                                                                                 /      \                                        7 + 4*x        /          \                                        7 + 4*x        /                           \                                                           (7 + 4*x)                                                                                                 /      \         7 + 4*x   / \                                        7 + 4*x        /         \                                                           (7 + 4*x)                                                                                                 /   \         7 + 4*x   / \                                        7 + 4*x        / \                                       7 + 4*x        /                    \                                        7 + 4*x        /     \                                        7 + 4*x        / \                                       7 + 4*x        /                                                               \                                                                                                         (7 + 4*x)        /                                                              \                                                           (7 + 4*x)                                                                                                 /                   \                                        7 + 4*x        /         \                                        7 + 4*x        / \                                       7 + 4*x        /      \                                        7 + 4*x        / \                                       7 + 4*x        /                \         7 + 4*x   / \                                        7 + 4*x        /                   \         7 + 4*x   / \                                        7 + 4*x        /                    \                                        7 + 4*x        /|
  /   -------- *|- ------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------ - ---------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------|
\/    7 + 4*x   |                             -5 + 3*x                                                                                                              7 + 4*x                                                                                                                                                                                                                                                 -5 + 3*x                                                                                                                                                                                                                                               -5 + 3*x                                                                                                              7 + 4*x                                                                 3                                                                                                                                  3                                                                                                                                          3                                                                                                                                  3                                                                                                                                                             2                                                                                                           2                                                                                             /       3\                                                                                                                                               /       3\                                                                                                                                                                                                      /       3\                                                                                                                                                  3                                                                                                   2                                                                                                                     /       3\                                                                                                 /       3\                                                                                           2                                                                                  /       3\                           |
                |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         9 + 2*x                                                                                                                            9 + 2*x                                                                                                                                    9 + 2*x                                                                                                                            9 + 2*x                                                                                                                                                    /       3\                                                                                                  /       3\                                                                                    (7 + 4*x)*\9 + 2*x /                                                                                                                                    (-5 + 3*x)*\9 + 2*x /                                                                                                                                                                                           (-5 + 3*x)*\9 + 2*x /                                                                                                                                           9 + 2*x                                                                                          /       3\                                                                                                           (-5 + 3*x)*\9 + 2*x /                                                                                       (7 + 4*x)*\9 + 2*x /                                                                                 /       3\                                                                         (7 + 4*x)*\9 + 2*x /                           |
                \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     \9 + 2*x /                                                                                                  \9 + 2*x /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \9 + 2*x /                                                                                                                                                                                                                                                                                                                            \9 + 2*x /                                                                                                                        /
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$$\frac{\sqrt{\frac{2 x^{3} + 9}{4 x + 7}} \left(- \frac{72 x^{4} \left(3 x - 5\right) \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{\left(2 x^{3} + 9\right)^{2}} + \frac{6 x^{2} \left(3 x - 5\right) \left(3 x^{2} - \frac{2 \left(2 x^{3} + 9\right)}{4 x + 7}\right) \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{\left(2 x^{3} + 9\right)^{2}} + \frac{48 x^{2} \left(3 x - 5\right) \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{\left(4 x + 7\right) \left(2 x^{3} + 9\right)} - \frac{108 x^{2} \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{2 x^{3} + 9} + \frac{24 x^{2} \left(- 54 x^{3} + \frac{6 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} - 36 x^{2} \left(3 x - 5\right) - 3 x \left(3 x - 5\right)^{2} - \frac{8 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} + \frac{12 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + \frac{6 \left(3 x - 5\right) \left(4 x^{3} + x^{2} \left(3 x - 5\right) + 18\right)}{4 x + 7} - 243\right)}{2 x^{3} + 9} + \frac{12 x^{2} \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right) \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)}{\left(2 x^{3} + 9\right)^{2}} + \frac{12 x \left(3 x - 5\right) \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{2 x^{3} + 9} - \frac{4 \left(3 x - 5\right) \left(3 x^{2} - \frac{2 \left(2 x^{3} + 9\right)}{4 x + 7}\right) \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{\left(4 x + 7\right) \left(2 x^{3} + 9\right)} + \frac{12 \left(3 x^{2} - \frac{2 \left(2 x^{3} + 9\right)}{4 x + 7}\right) \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{2 x^{3} + 9} - \frac{2 \left(3 x^{2} - \frac{2 \left(2 x^{3} + 9\right)}{4 x + 7}\right) \left(- 54 x^{3} + \frac{6 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} - 36 x^{2} \left(3 x - 5\right) - 3 x \left(3 x - 5\right)^{2} - \frac{8 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} + \frac{12 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + \frac{6 \left(3 x - 5\right) \left(4 x^{3} + x^{2} \left(3 x - 5\right) + 18\right)}{4 x + 7} - 243\right)}{2 x^{3} + 9} - \frac{\left(3 x^{2} - \frac{2 \left(2 x^{3} + 9\right)}{4 x + 7}\right) \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right) \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)}{\left(2 x^{3} + 9\right)^{2}} + \frac{72 \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{4 x + 7} - \frac{16 \left(- 54 x^{3} + \frac{6 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} - 36 x^{2} \left(3 x - 5\right) - 3 x \left(3 x - 5\right)^{2} - \frac{8 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} + \frac{12 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + \frac{6 \left(3 x - 5\right) \left(4 x^{3} + x^{2} \left(3 x - 5\right) + 18\right)}{4 x + 7} - 243\right)}{4 x + 7} - \frac{8 \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right) \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)}{\left(4 x + 7\right) \left(2 x^{3} + 9\right)} - \frac{108 \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{3 x - 5} + \frac{36 \left(- 54 x^{3} + \frac{6 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} - 36 x^{2} \left(3 x - 5\right) - 3 x \left(3 x - 5\right)^{2} - \frac{8 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} + \frac{12 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + \frac{6 \left(3 x - 5\right) \left(4 x^{3} + x^{2} \left(3 x - 5\right) + 18\right)}{4 x + 7} - 243\right)}{3 x - 5} - \frac{6 \left(- 108 x^{3} - \frac{32 x^{2} \left(3 x - 5\right)^{3}}{\left(4 x + 7\right)^{2}} + \frac{48 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} - 162 x^{2} \left(3 x - 5\right) + \frac{4 x \left(3 x - 5\right)^{3}}{4 x + 7} - 36 x \left(3 x - 5\right)^{2} - \left(3 x - 5\right)^{3} + \frac{32 \left(3 x - 5\right)^{3} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{3}} - \frac{64 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} - \frac{16 \left(3 x - 5\right)^{2} \left(4 x^{3} + x^{2} \left(3 x - 5\right) + 18\right)}{\left(4 x + 7\right)^{2}} + \frac{36 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + \frac{8 \left(3 x - 5\right) \left(18 x^{3} + 12 x^{2} \left(3 x - 5\right) + x \left(3 x - 5\right)^{2} + 81\right)}{4 x + 7} - 486\right)}{3 x - 5} + \frac{18 \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right) \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)}{\left(3 x - 5\right) \left(2 x^{3} + 9\right)} - \frac{2 \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right) \left(54 x^{3} - \frac{12 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} + 36 x^{2} \left(3 x - 5\right) + 3 x \left(3 x - 5\right)^{2} + \frac{8 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} - \frac{24 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 243\right)}{\left(3 x - 5\right) \left(2 x^{3} + 9\right)} - \frac{2 \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right) \left(- 54 x^{3} + \frac{6 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} - 36 x^{2} \left(3 x - 5\right) - 3 x \left(3 x - 5\right)^{2} - \frac{8 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} + \frac{12 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + \frac{6 \left(3 x - 5\right) \left(4 x^{3} + x^{2} \left(3 x - 5\right) + 18\right)}{4 x + 7} - 243\right)}{\left(3 x - 5\right) \left(2 x^{3} + 9\right)}\right)}{2 x^{3} + 9}$$

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Derivada de y=sqrt((3x-5)^4(2x^3+9)/(4x+7))

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Derivada de y=sqrt((3x-5)^4(2x^3+9)/(4x+7))

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