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Derivada de:
Derivada de (3x^4-x)^7
Derivada de (3x+6)^2
Derivada de (1+cos(x))/(1-cos(x))
Derivada de (2*x-9)/(x-5)
Expresiones idénticas
y=sqrt((tres x- cinco)^ cuatro (2x^3+ nueve)/(4x+ siete))^ uno / 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)) en el grado 1 dividir por 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)) en el grado uno dividir por siete
y=√((3x-5)^4(2x^3+9)/(4x+7))^1/7
y=sqrt((3x-5)4(2x3+9)/(4x+7))1/7
y=sqrt3x-542x3+9/4x+71/7
y=sqrt((3x-5)⁴(2x³+9)/(4x+7))^1/7
y=sqrt((3x-5) en el grado 4(2x en el grado 3+9)/(4x+7)) en el grado 1/7
y=sqrt3x-5^42x^3+9/4x+7^1/7
y=sqrt((3x-5)^4(2x^3+9) dividir por (4x+7))^1 dividir por 7
Expresiones semejantes
y=sqrt((3x-5)^4(2x^3-9)/(4x+7))^1/7
y=sqrt((3x-5)^4(2x^3+9)/(4x-7))^1/7
y=sqrt((3x+5)^4(2x^3+9)/(4x+7))^1/7

Derivada de la función/ y=sqrt((3x-5)^4(2x^3+9)/(4x+7))^1/7

Derivada de y=sqrt((3x-5)^4(2x^3+9)/(4x+7))^1/7

Solución

Ha introducido [src]

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

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

(sqrt(((3*x - 5)^4*(2*x^3 + 9))/(4*x + 7)))^(1/7)

Solución detallada

Sustituimos $u = \sqrt{\frac{\left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)}{4 x + 7}}$ .
Según el principio, aplicamos: $\sqrt[7]{u}$ tenemos $\frac{1}{7 u^{\frac{6}{7}}}$
Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \sqrt{\frac{\left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)}{4 x + 7}}$ :
1. Sustituimos $u = \frac{\left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)}{4 x + 7}$ .
2. Según el principio, aplicamos: $\sqrt{u}$ tenemos $\frac{1}{2 \sqrt{u}}$
3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \frac{\left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)}{4 x + 7}$ :
  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 $\frac{d}{d x} \left(3 x - 5\right)$ :
        
        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:
        
        La derivada de una constante $9$ 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: $x^{3}$ 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.
        
        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:
  
  $\frac{- 4 \left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right) + \left(4 x + 7\right) \left(6 x^{2} \left(3 x - 5\right)^{4} + 12 \left(3 x - 5\right)^{3} \left(2 x^{3} + 9\right)\right)}{2 \sqrt{\frac{2 x^{3} + 9}{4 x + 7}} \left(3 x - 5\right)^{2} \left(4 x + 7\right)^{2}}$
Como resultado de la secuencia de reglas:

$\frac{- 4 \left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right) + \left(4 x + 7\right) \left(6 x^{2} \left(3 x - 5\right)^{4} + 12 \left(3 x - 5\right)^{3} \left(2 x^{3} + 9\right)\right)}{14 \left(\frac{2 x^{3} + 9}{4 x + 7}\right)^{\frac{13}{14}} \left(3 x - 5\right)^{2} \left(4 x + 7\right)^{2} \left|{3 x - 5}\right|^{\frac{12}{7}}}$
Simplificamos:

$\frac{216 x^{5} - 39 x^{4} - 850 x^{3} + 1011 x^{2} + 594 x - 2340}{7 \left(\frac{2 x^{3} + 9}{4 x + 7}\right)^{\frac{13}{14}} \left(16 x^{2} + 56 x + 49\right) \left|{\left(3 x - 5\right)^{\frac{12}{7}}}\right|}$

Respuesta:

$\frac{216 x^{5} - 39 x^{4} - 850 x^{3} + 1011 x^{2} + 594 x - 2340}{7 \left(\frac{2 x^{3} + 9}{4 x + 7}\right)^{\frac{13}{14}} \left(16 x^{2} + 56 x + 49\right) \left|{\left(3 x - 5\right)^{\frac{12}{7}}}\right|}$

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/|
14/   --------------------- *(4*x + 7)*|------------------------------------------ - -----------------------|
\/           4*x + 7                   |               2*(4*x + 7)                                   2      |
                                       \                                                    (4*x + 7)       /
-------------------------------------------------------------------------------------------------------------
                                             /   3    \          4                                           
                                           7*\2*x  + 9/*(3*x - 5)

$$\frac{\sqrt[14]{\frac{\left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)}{4 x + 7}} \left(4 x + 7\right) \left(- \frac{2 \left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} + \frac{6 x^{2} \left(3 x - 5\right)^{4} + 12 \left(3 x - 5\right)^{3} \left(2 x^{3} + 9\right)}{2 \left(4 x + 7\right)}\right)}{7 \left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)}$$

Simplificar

Segunda derivada [src]

                              /                                                                    /                                                                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\\   /                                             /       3\\ /                                            /       3\\|
     __________               |     |          3      2              2*(-5 + 3*x)*\9 + 2*x /|   14*|-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                |  28*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|      |                                                                    2              7 + 4*x                        7 + 4*x                            7 + 4*x         |   84*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|   42*x *|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|   |-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------||
   /  9 + 2*x             2/7 |     \                                        7 + 4*x        /      \                                                           (7 + 4*x)                                                                                                 /      \                                        7 + 4*x        /         \                                        7 + 4*x        /   \                                        7 + 4*x        / \                                       7 + 4*x        /|
14/   -------- *|-5 + 3*x|   *|- ------------------------------------------------------------ - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------ + --------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------|
\/    7 + 4*x                 |                            7 + 4*x                                                                                                               -5 + 3*x                                                                                                              -5 + 3*x                                                                3                                                                                       /       3\                                               |
                              \                                                                                                                                                                                                                                                                                                                                         9 + 2*x                                                                             (-5 + 3*x)*\9 + 2*x /                                               /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                   /       3\                                                                                                                                                                                                                                                    
                                                                                                                                                                                                                                                     49*(-5 + 3*x)*\9 + 2*x /

$$\frac{\sqrt[14]{\frac{2 x^{3} + 9}{4 x + 7}} \left(\frac{42 x^{2} \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{2 x^{3} + 9} - \frac{28 \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{4 x + 7} + \frac{84 \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{3 x - 5} - \frac{14 \left(- 54 x^{3} + \frac{6 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} - 36 x^{2} \left(3 x - 5\right) - 3 x \left(3 x - 5\right)^{2} - \frac{8 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} + \frac{12 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + \frac{6 \left(3 x - 5\right) \left(4 x^{3} + x^{2} \left(3 x - 5\right) + 18\right)}{4 x + 7} - 243\right)}{3 x - 5} - \frac{\left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right) \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)}{\left(3 x - 5\right) \left(2 x^{3} + 9\right)}\right) \left|{3 x - 5}\right|^{\frac{2}{7}}}{49 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}$$

Simplificar

Tercera derivada [src]

                /                                                                                                   /                                                                                  2 /       3\       2           3                2 /        3    2           \                 3                /         3               2       2           \                3 /       3\                 /       3\       2           2\                      /                                                                2 /       3\      2           2                /        3    2           \                 /       3\\                                                                                                       /                                                                2 /       3\      2           2                /        3    2           \                 /       3\\                                                                                     /                                                                2 /       3\      2           2                /        3    2           \                 /       3\\                                                                                                                                                                                                                                                                                                                                                                                                                                                                      /         /       3\\ /                                                                2 /       3\      2           2                /        3    2           \                 /       3\\                    /                                             /       3\\ /                                                                 /       3\       2           2               2 /       3\\                    /                                            /       3\\ /                                                                2 /       3\      2           2                /        3    2           \                 /       3\\                                                                                                                                                                                                                                                                                                                                                                                                                                                           /                                                                2 /       3\      2           2                /        3    2           \                 /       3\\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                \
                |                     /                                             /       3\\                 2/7 |                 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) |                  2/7 |           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\\                 2/7 |           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   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\\                2/7 |   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 /|                2/7 |          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 /|                2/7 |         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\\                        2           2/7 |           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\\|
     __________ |                 2/7 |          3      2              2*(-5 + 3*x)*\9 + 2*x /|   294*|-5 + 3*x|   *|-486 - (-5 + 3*x)  - 108*x  - 162*x *(-5 + 3*x) - 36*x*(-5 + 3*x)  - ------------------------- - ----------------- - ------------------------------------------ + --------------- + ------------------------------------------------------------ + ------------------------- + ------------------------ + -----------------|   2352*|-5 + 3*x|   *|-243 - 54*x  - 36*x *(-5 + 3*x) - 3*x*(-5 + 3*x)  - ------------------------ + ---------------- + ---------------------------------------- + ------------------------|         4           2/7 |          3      2              2*(-5 + 3*x)*\9 + 2*x /|   784*|-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 /|                  84*|-243 - 54*x  - 36*x *(-5 + 3*x) - 3*x*(-5 + 3*x)  - ------------------------ + ---------------- + ---------------------------------------- + ------------------------|*sign(-5 + 3*x)       |          3      2              2*(-5 + 3*x)*\9 + 2*x /|                                  2/7 |          3      2              2*(-5 + 3*x)*\9 + 2*x /|                  2/7 |          3      2              2*(-5 + 3*x)*\9 + 2*x /|         2           2/7 |          3      2              2*(-5 + 3*x)*\9 + 2*x /|                2/7 |   2   2*\9 + 2*x /| |          3      2              2*(-5 + 3*x)*\9 + 2*x /|   14*|-5 + 3*x|   *|3*x  - ------------|*|-243 - 54*x  - 36*x *(-5 + 3*x) - 3*x*(-5 + 3*x)  - ------------------------ + ---------------- + ---------------------------------------- + ------------------------|   14*|-5 + 3*x|   *|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|*|243 + 54*x  + 3*x*(-5 + 3*x)  + 36*x *(-5 + 3*x) - ------------------------ - ----------------- + ------------------------|   14*|-5 + 3*x|   *|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|*|-243 - 54*x  - 36*x *(-5 + 3*x) - 3*x*(-5 + 3*x)  - ------------------------ + ---------------- + ---------------------------------------- + ------------------------|       2           2/7 |   2   2*\9 + 2*x /| |          3      2              2*(-5 + 3*x)*\9 + 2*x /|                2/7 |   2   2*\9 + 2*x /| |          3      2              2*(-5 + 3*x)*\9 + 2*x /|                 2/7 |          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 /|                  1176*x *|-5 + 3*x|   *|-243 - 54*x  - 36*x *(-5 + 3*x) - 3*x*(-5 + 3*x)  - ------------------------ + ---------------- + ---------------------------------------- + ------------------------|         2           2/7 |          3      2              2*(-5 + 3*x)*\9 + 2*x /|             2/7 |   2   2*\9 + 2*x /| |          3      2              2*(-5 + 3*x)*\9 + 2*x /| |         3      2              2*(-5 + 3*x)*\9 + 2*x /|                2/7 |          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           2/7 |          3      2              2*(-5 + 3*x)*\9 + 2*x /| |         3      2              2*(-5 + 3*x)*\9 + 2*x /||
    /        3  |  8820*|-5 + 3*x|   *|-54 - 12*x  - 3*x *(-5 + 3*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         |   3528*x *|-5 + 3*x|   *|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|                     |                                                                    2              7 + 4*x                        7 + 4*x                            7 + 4*x         |   168*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|*sign(-5 + 3*x)      |                                                                    2              7 + 4*x                        7 + 4*x                            7 + 4*x         |                  504*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|*sign(-5 + 3*x)   588*x*|-5 + 3*x|   *|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|   4704*|-5 + 3*x|   *|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|   7056*x *|-5 + 3*x|   *|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|   28*|-5 + 3*x|   *|3*x  - ------------|*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|                    \         7 + 4*x   / |                                                                    2              7 + 4*x                        7 + 4*x                            7 + 4*x         |                    \                                        7 + 4*x        / |                                                           7 + 4*x                 7 + 4*x                        2       |                    \                                       7 + 4*x        / |                                                                    2              7 + 4*x                        7 + 4*x                            7 + 4*x         |   42*x *|-5 + 3*x|   *|3*x  - ------------|*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|   84*|-5 + 3*x|   *|3*x  - ------------|*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|   168*|-5 + 3*x|   *|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|   252*x *|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|*sign(-5 + 3*x)                         |                                                                    2              7 + 4*x                        7 + 4*x                            7 + 4*x         |   2352*x *|-5 + 3*x|   *|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|   |-5 + 3*x|   *|3*x  - ------------|*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|   56*|-5 + 3*x|   *|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|   6*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|*sign(-5 + 3*x)   84*x *|-5 + 3*x|   *|-54 - 12*x  - 3*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        / \                                       7 + 4*x        /     \                                        7 + 4*x        / \                                       7 + 4*x        /                                      \                                        7 + 4*x        / \                                       7 + 4*x        /|
14/   -------- *|- ---------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------- + ----------------------------------------------------------------------------- + ---------------------------------------------------------------------------- - ------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------ - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------ - ----------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------|
\/    7 + 4*x   |                                            2                                                                                                                                                                                                                2                                                                                                                                                                                                                                                                      2                                                                                                                                       2                                                                                                                        (-5 + 3*x)*(7 + 4*x)                                                                                                                                   5/7                                                                                                                                    5/7                                                                                                                                  5/7                                                                       3                                                                 (-5 + 3*x)*(7 + 4*x)                                                                       /       3\                                                                                /       3\                                                                                                                                                /       3\                                                                                                                                                                                                   2 /       3\                                                                                                                                                                                                                   2 /       3\                                                                                                                                                                      2                                                                                               /       3\                                                                                                          2 /       3\                                                                                      /       3\           5/7                                                                                                                             /       3\                                                                                                                               /       3\                                                                                                                     2                                                                                                                                          /       3\                                                                                                                /       3\           5/7                                                                                                                                2                                                        |
                |                                  (-5 + 3*x)                                                                                                                                                                                                       (-5 + 3*x)                                                                                                                                                                                                                                                             (-5 + 3*x)                                                                                                                              /       3\                                                                                                                                                                                                                                                            (7 + 4*x)*|-5 + 3*x|                                                                                                                  (-5 + 3*x)*|-5 + 3*x|                                                                                                                (-5 + 3*x)*|-5 + 3*x|                                                                   9 + 2*x                                                                                                                                                  (-5 + 3*x)*\9 + 2*x /                                                                      (7 + 4*x)*\9 + 2*x /                                                                                                                                     (-5 + 3*x)*\9 + 2*x /                                                                                                                                                                                         (-5 + 3*x) *\9 + 2*x /                                                                                                                                                                                                         (-5 + 3*x) *\9 + 2*x /                                                                                                                                                            /       3\                                                                                     (-5 + 3*x)*\9 + 2*x /                                                                                                (-5 + 3*x) *\9 + 2*x /                                                                                      \9 + 2*x /*|-5 + 3*x|                                                                                                                     (-5 + 3*x)*\9 + 2*x /                                                                                                                     (7 + 4*x)*\9 + 2*x /                                                                                                           /       3\                                                                                                                      (-5 + 3*x)*(7 + 4*x)*\9 + 2*x /                                                                                                     (-5 + 3*x)*\9 + 2*x /*|-5 + 3*x|                                                                                                                         /       3\                                                         |
                \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  \9 + 2*x /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           \9 + 2*x /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              (-5 + 3*x)*\9 + 2*x /                                                                                                                                                                                                                                                                                                                                                                                                        (-5 + 3*x)*\9 + 2*x /                                                         /
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                /       3\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 343*(-5 + 3*x)*\9 + 2*x /

$$\frac{\sqrt[14]{\frac{2 x^{3} + 9}{4 x + 7}} \left(- \frac{3528 x^{4} \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|^{\frac{2}{7}}}{\left(2 x^{3} + 9\right)^{2}} + \frac{42 x^{2} \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|{3 x - 5}\right|^{\frac{2}{7}}}{\left(2 x^{3} + 9\right)^{2}} + \frac{252 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) \operatorname{sign}{\left(3 x - 5 \right)}}{\left(2 x^{3} + 9\right) \left|{3 x - 5}\right|^{\frac{5}{7}}} + \frac{2352 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|{3 x - 5}\right|^{\frac{2}{7}}}{\left(4 x + 7\right) \left(2 x^{3} + 9\right)} - \frac{7056 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|{3 x - 5}\right|^{\frac{2}{7}}}{\left(3 x - 5\right) \left(2 x^{3} + 9\right)} + \frac{1176 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) \left|{3 x - 5}\right|^{\frac{2}{7}}}{\left(3 x - 5\right) \left(2 x^{3} + 9\right)} + \frac{84 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|{3 x - 5}\right|^{\frac{2}{7}}}{\left(3 x - 5\right) \left(2 x^{3} + 9\right)^{2}} + \frac{588 x \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|^{\frac{2}{7}}}{2 x^{3} + 9} - \frac{28 \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|{3 x - 5}\right|^{\frac{2}{7}}}{\left(4 x + 7\right) \left(2 x^{3} + 9\right)} - \frac{168 \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) \operatorname{sign}{\left(3 x - 5 \right)}}{\left(4 x + 7\right) \left|{3 x - 5}\right|^{\frac{5}{7}}} + \frac{84 \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|{3 x - 5}\right|^{\frac{2}{7}}}{\left(3 x - 5\right) \left(2 x^{3} + 9\right)} - \frac{14 \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) \left|{3 x - 5}\right|^{\frac{2}{7}}}{\left(3 x - 5\right) \left(2 x^{3} + 9\right)} - \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|{3 x - 5}\right|^{\frac{2}{7}}}{\left(3 x - 5\right) \left(2 x^{3} + 9\right)^{2}} + \frac{504 \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) \operatorname{sign}{\left(3 x - 5 \right)}}{\left(3 x - 5\right) \left|{3 x - 5}\right|^{\frac{5}{7}}} - \frac{84 \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) \operatorname{sign}{\left(3 x - 5 \right)}}{\left(3 x - 5\right) \left|{3 x - 5}\right|^{\frac{5}{7}}} - \frac{6 \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) \operatorname{sign}{\left(3 x - 5 \right)}}{\left(3 x - 5\right) \left(2 x^{3} + 9\right) \left|{3 x - 5}\right|^{\frac{5}{7}}} + \frac{4704 \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|^{\frac{2}{7}}}{\left(3 x - 5\right) \left(4 x + 7\right)} - \frac{784 \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|^{\frac{2}{7}}}{\left(3 x - 5\right) \left(4 x + 7\right)} - \frac{56 \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|^{\frac{2}{7}}}{\left(3 x - 5\right) \left(4 x + 7\right) \left(2 x^{3} + 9\right)} - \frac{8820 \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|^{\frac{2}{7}}}{\left(3 x - 5\right)^{2}} + \frac{2352 \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|^{\frac{2}{7}}}{\left(3 x - 5\right)^{2}} - \frac{294 \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) \left|{3 x - 5}\right|^{\frac{2}{7}}}{\left(3 x - 5\right)^{2}} + \frac{168 \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|^{\frac{2}{7}}}{\left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)} - \frac{14 \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|^{\frac{2}{7}}}{\left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)} - \frac{14 \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|^{\frac{2}{7}}}{\left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}\right)}{343 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}$$

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Derivada de y=sqrt((3x-5)^4(2x^3+9)/(4x+7))^1/7

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Derivada de y=sqrt((3x-5)^4(2x^3+9)/(4x+7))^1/7

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