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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

Función f() - derivada -er orden en el punto
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Solución

Ha introducido [src] 
      ______________________________
     /      _______________________ 
    /      /          4 /   3    \  
   /      /  (3*x - 5) *\2*x  + 9/  
7 /      /   ---------------------  
\/     \/           4*x + 7
(3x−5)4(2x3+9)4x+77\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

  1. Sustituimos u=(3x−5)4(2x3+9)4x+7u = \sqrt{\frac{\left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)}{4 x + 7}}.

  2. Según el principio, aplicamos: u7\sqrt[7]{u} tenemos 17u67\frac{1}{7 u^{\frac{6}{7}}}

  3. Luego se aplica una cadena de reglas. Multiplicamos por ddx(3x−5)4(2x3+9)4x+7\frac{d}{d x} \sqrt{\frac{\left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)}{4 x + 7}}:

    1. Sustituimos u=(3x−5)4(2x3+9)4x+7u = \frac{\left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)}{4 x + 7}.

    2. Según el principio, aplicamos: u\sqrt{u} tenemos 12u\frac{1}{2 \sqrt{u}}

    3. Luego se aplica una cadena de reglas. Multiplicamos por ddx(3x−5)4(2x3+9)4x+7\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:

        ddxf(x)g(x)=−f(x)ddxg(x)+g(x)ddxf(x)g2(x)\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(x)=(3x−5)4(2x3+9)f{\left(x \right)} = \left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right) y g(x)=4x+7g{\left(x \right)} = 4 x + 7.

        Para calcular ddxf(x)\frac{d}{d x} f{\left(x \right)}:

        1. Se aplica la regla de la derivada de una multiplicación:

          ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x)\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(x)=(3x−5)4f{\left(x \right)} = \left(3 x - 5\right)^{4}; calculamos ddxf(x)\frac{d}{d x} f{\left(x \right)}:

          1. Sustituimos u=3x−5u = 3 x - 5.

          2. Según el principio, aplicamos: u4u^{4} tenemos 4u34 u^{3}

          3. Luego se aplica una cadena de reglas. Multiplicamos por ddx(3x−5)\frac{d}{d x} \left(3 x - 5\right):

            1. diferenciamos 3x−53 x - 5 miembro por miembro:

              1. La derivada de una constante −5-5 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: xx tenemos 11

                Entonces, como resultado: 33

              Como resultado de: 33

            Como resultado de la secuencia de reglas:

            12(3x−5)312 \left(3 x - 5\right)^{3}

          g(x)=2x3+9g{\left(x \right)} = 2 x^{3} + 9; calculamos ddxg(x)\frac{d}{d x} g{\left(x \right)}:

          1. diferenciamos 2x3+92 x^{3} + 9 miembro por miembro:

            1. La derivada de una constante 99 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: x3x^{3} tenemos 3x23 x^{2}

              Entonces, como resultado: 6x26 x^{2}

            Como resultado de: 6x26 x^{2}

          Como resultado de: 6x2(3x−5)4+12(3x−5)3(2x3+9)6 x^{2} \left(3 x - 5\right)^{4} + 12 \left(3 x - 5\right)^{3} \left(2 x^{3} + 9\right)

        Para calcular ddxg(x)\frac{d}{d x} g{\left(x \right)}:

        1. diferenciamos 4x+74 x + 7 miembro por miembro:

          1. La derivada de una constante 77 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: xx tenemos 11

            Entonces, como resultado: 44

          Como resultado de: 44

        Ahora aplicamos la regla de la derivada de una divesión:

        −4(3x−5)4(2x3+9)+(4x+7)(6x2(3x−5)4+12(3x−5)3(2x3+9))(4x+7)2\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:

      −4(3x−5)4(2x3+9)+(4x+7)(6x2(3x−5)4+12(3x−5)3(2x3+9))22x3+94x+7(3x−5)2(4x+7)2\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:

    −4(3x−5)4(2x3+9)+(4x+7)(6x2(3x−5)4+12(3x−5)3(2x3+9))14(2x3+94x+7)1314(3x−5)2(4x+7)2∣3x−5∣127\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}}}

  4. Simplificamos:

    216x5−39x4−850x3+1011x2+594x−23407(2x3+94x+7)1314(16x2+56x+49)∣(3x−5)127∣\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:

216x5−39x4−850x3+1011x2+594x−23407(2x3+94x+7)1314(16x2+56x+49)∣(3x−5)127∣\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
02468-8-6-4-2-10105-5
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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)
(3x−5)4(2x3+9)4x+714(4x+7)(−2(3x−5)4(2x3+9)(4x+7)2+6x2(3x−5)4+12(3x−5)3(2x3+9)2(4x+7))7(3x−5)4(2x3+9)\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 /                                               /
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                                                                                                                                                                                                                                                                   /       3\                                                                                                                                                                                                                                                    
                                                                                                                                                                                                                                                     49*(-5 + 3*x)*\9 + 2*x /
2x3+94x+714(42x2(−12x3−3x2(3x−5)+2(3x−5)(2x3+9)4x+7−54)2x3+9−28(−12x3−3x2(3x−5)+2(3x−5)(2x3+9)4x+7−54)4x+7+84(−12x3−3x2(3x−5)+2(3x−5)(2x3+9)4x+7−54)3x−5−14(−54x3+6x2(3x−5)24x+7−36x2(3x−5)−3x(3x−5)2−8(3x−5)2(2x3+9)(4x+7)2+12(3x−5)(2x3+9)4x+7+6(3x−5)(4x3+x2(3x−5)+18)4x+7−243)3x−5−(−12x3−3x2(3x−5)+2(3x−5)(2x3+9)4x+7−54)(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)(3x−5)(2x3+9))∣3x−5∣2749(3x−5)(2x3+9)\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 /
2x3+94x+714(−3528x4(−12x3−3x2(3x−5)+2(3x−5)(2x3+9)4x+7−54)∣3x−5∣27(2x3+9)2+42x2(3x2−2(2x3+9)4x+7)(−12x3−3x2(3x−5)+2(3x−5)(2x3+9)4x+7−54)∣3x−5∣27(2x3+9)2+252x2(−12x3−3x2(3x−5)+2(3x−5)(2x3+9)4x+7−54)sign⁡(3x−5)(2x3+9)∣3x−5∣57+2352x2(−12x3−3x2(3x−5)+2(3x−5)(2x3+9)4x+7−54)∣3x−5∣27(4x+7)(2x3+9)−7056x2(−12x3−3x2(3x−5)+2(3x−5)(2x3+9)4x+7−54)∣3x−5∣27(3x−5)(2x3+9)+1176x2(−54x3+6x2(3x−5)24x+7−36x2(3x−5)−3x(3x−5)2−8(3x−5)2(2x3+9)(4x+7)2+12(3x−5)(2x3+9)4x+7+6(3x−5)(4x3+x2(3x−5)+18)4x+7−243)∣3x−5∣27(3x−5)(2x3+9)+84x2(−12x3−3x2(3x−5)+2(3x−5)(2x3+9)4x+7−54)(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)∣3x−5∣27(3x−5)(2x3+9)2+588x(−12x3−3x2(3x−5)+2(3x−5)(2x3+9)4x+7−54)∣3x−5∣272x3+9−28(3x2−2(2x3+9)4x+7)(−12x3−3x2(3x−5)+2(3x−5)(2x3+9)4x+7−54)∣3x−5∣27(4x+7)(2x3+9)−168(−12x3−3x2(3x−5)+2(3x−5)(2x3+9)4x+7−54)sign⁡(3x−5)(4x+7)∣3x−5∣57+84(3x2−2(2x3+9)4x+7)(−12x3−3x2(3x−5)+2(3x−5)(2x3+9)4x+7−54)∣3x−5∣27(3x−5)(2x3+9)−14(3x2−2(2x3+9)4x+7)(−54x3+6x2(3x−5)24x+7−36x2(3x−5)−3x(3x−5)2−8(3x−5)2(2x3+9)(4x+7)2+12(3x−5)(2x3+9)4x+7+6(3x−5)(4x3+x2(3x−5)+18)4x+7−243)∣3x−5∣27(3x−5)(2x3+9)−(3x2−2(2x3+9)4x+7)(−12x3−3x2(3x−5)+2(3x−5)(2x3+9)4x+7−54)(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)∣3x−5∣27(3x−5)(2x3+9)2+504(−12x3−3x2(3x−5)+2(3x−5)(2x3+9)4x+7−54)sign⁡(3x−5)(3x−5)∣3x−5∣57−84(−54x3+6x2(3x−5)24x+7−36x2(3x−5)−3x(3x−5)2−8(3x−5)2(2x3+9)(4x+7)2+12(3x−5)(2x3+9)4x+7+6(3x−5)(4x3+x2(3x−5)+18)4x+7−243)sign⁡(3x−5)(3x−5)∣3x−5∣57−6(−12x3−3x2(3x−5)+2(3x−5)(2x3+9)4x+7−54)(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)sign⁡(3x−5)(3x−5)(2x3+9)∣3x−5∣57+4704(−12x3−3x2(3x−5)+2(3x−5)(2x3+9)4x+7−54)∣3x−5∣27(3x−5)(4x+7)−784(−54x3+6x2(3x−5)24x+7−36x2(3x−5)−3x(3x−5)2−8(3x−5)2(2x3+9)(4x+7)2+12(3x−5)(2x3+9)4x+7+6(3x−5)(4x3+x2(3x−5)+18)4x+7−243)∣3x−5∣27(3x−5)(4x+7)−56(−12x3−3x2(3x−5)+2(3x−5)(2x3+9)4x+7−54)(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)∣3x−5∣27(3x−5)(4x+7)(2x3+9)−8820(−12x3−3x2(3x−5)+2(3x−5)(2x3+9)4x+7−54)∣3x−5∣27(3x−5)2+2352(−54x3+6x2(3x−5)24x+7−36x2(3x−5)−3x(3x−5)2−8(3x−5)2(2x3+9)(4x+7)2+12(3x−5)(2x3+9)4x+7+6(3x−5)(4x3+x2(3x−5)+18)4x+7−243)∣3x−5∣27(3x−5)2−294(−108x3−32x2(3x−5)3(4x+7)2+48x2(3x−5)24x+7−162x2(3x−5)+4x(3x−5)34x+7−36x(3x−5)2−(3x−5)3+32(3x−5)3(2x3+9)(4x+7)3−64(3x−5)2(2x3+9)(4x+7)2−16(3x−5)2(4x3+x2(3x−5)+18)(4x+7)2+36(3x−5)(2x3+9)4x+7+8(3x−5)(18x3+12x2(3x−5)+x(3x−5)2+81)4x+7−486)∣3x−5∣27(3x−5)2+168(−12x3−3x2(3x−5)+2(3x−5)(2x3+9)4x+7−54)(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)∣3x−5∣27(3x−5)2(2x3+9)−14(−12x3−3x2(3x−5)+2(3x−5)(2x3+9)4x+7−54)(54x3−12x2(3x−5)24x+7+36x2(3x−5)+3x(3x−5)2+8(3x−5)2(2x3+9)(4x+7)2−24(3x−5)(2x3+9)4x+7+243)∣3x−5∣27(3x−5)2(2x3+9)−14(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)(−54x3+6x2(3x−5)24x+7−36x2(3x−5)−3x(3x−5)2−8(3x−5)2(2x3+9)(4x+7)2+12(3x−5)(2x3+9)4x+7+6(3x−5)(4x3+x2(3x−5)+18)4x+7−243)∣3x−5∣27(3x−5)2(2x3+9))343(3x−5)(2x3+9)\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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