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

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

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
       _______________________
      /          4 /   3    \ 
     /  (3*x - 5) *\2*x  + 9/ 
7*  /   --------------------- 
  \/           4*x + 7
7(3x−5)4(2x3+9)4x+77 \sqrt{\frac{\left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)}{4 x + 7}} 
7*sqrt(((3*x - 5)^4*(2*x^3 + 9))/(4*x + 7))
Solución detallada

  1. La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.

    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}}

    Entonces, como resultado: 7(−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{7 \left(- 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)\right)}{2 \sqrt{\frac{2 x^{3} + 9}{4 x + 7}} \left(3 x - 5\right)^{2} \left(4 x + 7\right)^{2}}

  2. Simplificamos:

    7(216x5−39x4−850x3+1011x2+594x−2340)2x3+94x+7(16x2+56x+49)\frac{7 \left(216 x^{5} - 39 x^{4} - 850 x^{3} + 1011 x^{2} + 594 x - 2340\right)}{\sqrt{\frac{2 x^{3} + 9}{4 x + 7}} \left(16 x^{2} + 56 x + 49\right)}

Respuesta:

7(216x5−39x4−850x3+1011x2+594x−2340)2x3+94x+7(16x2+56x+49)\frac{7 \left(216 x^{5} - 39 x^{4} - 850 x^{3} + 1011 x^{2} + 594 x - 2340\right)}{\sqrt{\frac{2 x^{3} + 9}{4 x + 7}} \left(16 x^{2} + 56 x + 49\right)}

Gráfica
02468-8-6-4-2-1010-100000100000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
       __________                                                                                            
      /    3                           /   2          4               3 /   3    \              4 /   3    \\
     /  2*x  + 9           2           |6*x *(3*x - 5)  + 12*(3*x - 5) *\2*x  + 9/   2*(3*x - 5) *\2*x  + 9/|
7*  /   -------- *(3*x - 5) *(4*x + 7)*|------------------------------------------ - -----------------------|
  \/    4*x + 7                        |               2*(4*x + 7)                                   2      |
                                       \                                                    (4*x + 7)       /
-------------------------------------------------------------------------------------------------------------
                                            /   3    \          4                                            
                                            \2*x  + 9/*(3*x - 5)
72x3+94x+7(3x−5)2(4x+7)(−2(3x−5)4(2x3+9)(4x+7)2+6x2(3x−5)4+12(3x−5)3(2x3+9)2(4x+7))(3x−5)4(2x3+9)\frac{7 \sqrt{\frac{2 x^{3} + 9}{4 x + 7}} \left(3 x - 5\right)^{2} \left(4 x + 7\right) \left(- \frac{2 \left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} + \frac{6 x^{2} \left(3 x - 5\right)^{4} + 12 \left(3 x - 5\right)^{3} \left(2 x^{3} + 9\right)}{2 \left(4 x + 7\right)}\right)}{\left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)}
Simplificar
Segunda derivada [src] 
                   /                                                                      2                                                                                                                                                                                                                                                                                    \
                   |              /                                            /       3\\                                                                                  /                                            /       3\\                                                                                   /                                            /       3\\|
        __________ |              |         3      2              2*(-5 + 3*x)*\9 + 2*x /|                                                                                  |         3      2              2*(-5 + 3*x)*\9 + 2*x /|                                                                      2            |         3      2              2*(-5 + 3*x)*\9 + 2*x /||
       /        3  |              |54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|                                                      2 /       3\   4*(-5 + 3*x)*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|       2           2                 /        3    2           \   6*x *(-5 + 3*x)*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------||
      /  9 + 2*x   |          3   \                                       7 + 4*x        /        2                            2   16*(-5 + 3*x) *\9 + 2*x /                \                                       7 + 4*x        /   12*x *(-5 + 3*x)    12*(-5 + 3*x)*\18 + 4*x  + x *(-5 + 3*x)/                   \                                       7 + 4*x        /|
-7*  /   -------- *|162 + 36*x  - --------------------------------------------------------- - 36*x *(-5 + 3*x) - 6*x*(-5 + 3*x)  - ------------------------- - --------------------------------------------------------------------- + ----------------- + ----------------------------------------- + ------------------------------------------------------------------------|
   \/    7 + 4*x   |                                              3                                                                                 2                                         7 + 4*x                                       7 + 4*x                         7 + 4*x                                                           3                                |
                   \                                       9 + 2*x                                                                         (7 + 4*x)                                                                                                                                                                                   9 + 2*x                                 /
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                                                                                                                                                                                           3                                                                                                                                                                                    
                                                                                                                                                                                    9 + 2*x
−72x3+94x+7(36x3+12x2(3x−5)24x+7−36x2(3x−5)+6x2(3x−5)(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)2x3+9−6x(3x−5)2−16(3x−5)2(2x3+9)(4x+7)2+12(3x−5)(4x3+x2(3x−5)+18)4x+7−4(3x−5)(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)4x+7+162−(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)22x3+9)2x3+9- \frac{7 \sqrt{\frac{2 x^{3} + 9}{4 x + 7}} \left(36 x^{3} + \frac{12 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} - 36 x^{2} \left(3 x - 5\right) + \frac{6 x^{2} \left(3 x - 5\right) \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)}{2 x^{3} + 9} - 6 x \left(3 x - 5\right)^{2} - \frac{16 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} + \frac{12 \left(3 x - 5\right) \left(4 x^{3} + x^{2} \left(3 x - 5\right) + 18\right)}{4 x + 7} - \frac{4 \left(3 x - 5\right) \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)}{4 x + 7} + 162 - \frac{\left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)^{2}}{2 x^{3} + 9}\right)}{2 x^{3} + 9}
Simplificar
Tercera derivada [src] 
                   /                                                                    /                                                                 /       3\      2           2                /        3    2           \               2 /       3\\     /                                                                        2           2                 /       3\                3 /       3\                /         3               2       2           \                 3                2 /        3    2           \       2           3                2 /       3\\      /                                                                 /       3\      2           2                /        3    2           \               2 /       3\\                                                                                                                         2                                                                                                                                                     2     /         /       3\\ /                                                                 /       3\      2           2                /        3    2           \               2 /       3\\                                                                 2                                                                                                                                                  2         /                                                                 /       3\      2           2                /        3    2           \               2 /       3\\                                                                                 /                                            /       3\\ /                                                                 /       3\       2           2               2 /       3\\     /                                            /       3\\ /                                                                 /       3\      2           2                /        3    2           \               2 /       3\\                                                                                                                                                                                                                                                                                                                                                      \
                   |      /                                            /       3\\      |          3                 2       2              12*(-5 + 3*x)*\9 + 2*x /   6*x *(-5 + 3*x)    6*(-5 + 3*x)*\18 + 4*x  + x *(-5 + 3*x)/   8*(-5 + 3*x) *\9 + 2*x /|     |                3        3                  2        2              48*x *(-5 + 3*x)    36*(-5 + 3*x)*\9 + 2*x /   32*(-5 + 3*x) *\9 + 2*x /   8*(-5 + 3*x)*\81 + 18*x  + x*(-5 + 3*x)  + 12*x *(-5 + 3*x)/   4*x*(-5 + 3*x)    16*(-5 + 3*x) *\18 + 4*x  + x *(-5 + 3*x)/   32*x *(-5 + 3*x)    64*(-5 + 3*x) *\9 + 2*x /|      |          3                 2       2              12*(-5 + 3*x)*\9 + 2*x /   6*x *(-5 + 3*x)    6*(-5 + 3*x)*\18 + 4*x  + x *(-5 + 3*x)/   8*(-5 + 3*x) *\9 + 2*x /|      /                                            /       3\\   /                                            /       3\\  /         /       3\\          /                                            /       3\\     /                                            /       3\\      |   2   2*\9 + 2*x /| |          3                 2       2              12*(-5 + 3*x)*\9 + 2*x /   6*x *(-5 + 3*x)    6*(-5 + 3*x)*\18 + 4*x  + x *(-5 + 3*x)/   8*(-5 + 3*x) *\9 + 2*x /|         /                                            /       3\\       /         /       3\\ /                                            /       3\\      /                                            /       3\\        2 |          3                 2       2              12*(-5 + 3*x)*\9 + 2*x /   6*x *(-5 + 3*x)    6*(-5 + 3*x)*\18 + 4*x  + x *(-5 + 3*x)/   8*(-5 + 3*x) *\9 + 2*x /|                    /                                            /       3\\     |         3      2              2*(-5 + 3*x)*\9 + 2*x /| |          3                 2       2              24*(-5 + 3*x)*\9 + 2*x /   12*x *(-5 + 3*x)    8*(-5 + 3*x) *\9 + 2*x /|     |         3      2              2*(-5 + 3*x)*\9 + 2*x /| |          3                 2       2              12*(-5 + 3*x)*\9 + 2*x /   6*x *(-5 + 3*x)    6*(-5 + 3*x)*\18 + 4*x  + x *(-5 + 3*x)/   8*(-5 + 3*x) *\9 + 2*x /|                   /                                            /       3\\                /         /       3\\ /                                            /       3\\                   /         /       3\\ /                                            /       3\\                    /                                            /       3\\|
        __________ |      |         3      2              2*(-5 + 3*x)*\9 + 2*x /|   16*|243 + 54*x  + 3*x*(-5 + 3*x)  + 36*x *(-5 + 3*x) - ------------------------ - ---------------- - ---------------------------------------- + ------------------------|   6*|486 + (-5 + 3*x)  + 108*x  + 36*x*(-5 + 3*x)  + 162*x *(-5 + 3*x) - ----------------- - ------------------------ - ------------------------- - ------------------------------------------------------------ - --------------- + ------------------------------------------ + ----------------- + -------------------------|   36*|243 + 54*x  + 3*x*(-5 + 3*x)  + 36*x *(-5 + 3*x) - ------------------------ - ---------------- - ---------------------------------------- + ------------------------|      |         3      2              2*(-5 + 3*x)*\9 + 2*x /|   |         3      2              2*(-5 + 3*x)*\9 + 2*x /|  |   2   2*\9 + 2*x /|        2 |         3      2              2*(-5 + 3*x)*\9 + 2*x /|     |         3      2              2*(-5 + 3*x)*\9 + 2*x /|    2*|3*x  - ------------|*|243 + 54*x  + 3*x*(-5 + 3*x)  + 36*x *(-5 + 3*x) - ------------------------ - ---------------- - ---------------------------------------- + ------------------------|       2 |         3      2              2*(-5 + 3*x)*\9 + 2*x /|       |   2   2*\9 + 2*x /| |         3      2              2*(-5 + 3*x)*\9 + 2*x /|      |         3      2              2*(-5 + 3*x)*\9 + 2*x /|    24*x *|243 + 54*x  + 3*x*(-5 + 3*x)  + 36*x *(-5 + 3*x) - ------------------------ - ---------------- - ---------------------------------------- + ------------------------|       4            |         3      2              2*(-5 + 3*x)*\9 + 2*x /|   2*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|*|243 + 54*x  + 3*x*(-5 + 3*x)  + 36*x *(-5 + 3*x) - ------------------------ - ----------------- + ------------------------|   2*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|*|243 + 54*x  + 3*x*(-5 + 3*x)  + 36*x *(-5 + 3*x) - ------------------------ - ---------------- - ---------------------------------------- + ------------------------|                   |         3      2              2*(-5 + 3*x)*\9 + 2*x /|                |   2   2*\9 + 2*x /| |         3      2              2*(-5 + 3*x)*\9 + 2*x /|      2            |   2   2*\9 + 2*x /| |         3      2              2*(-5 + 3*x)*\9 + 2*x /|       2            |         3      2              2*(-5 + 3*x)*\9 + 2*x /||
       /        3  |  108*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|      |                                                           7 + 4*x                7 + 4*x                        7 + 4*x                                    2       |     |                                                                         7 + 4*x                7 + 4*x                             3                                    7 + 4*x                                  7 + 4*x                                2                                2                       2       |      |                                                           7 + 4*x                7 + 4*x                        7 + 4*x                                    2       |   72*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|   |54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------| *|3*x  - ------------|   108*x *|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|   8*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|      \         7 + 4*x   / |                                                           7 + 4*x                7 + 4*x                        7 + 4*x                                    2       |   12*x *|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|    12*|3*x  - ------------|*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|   18*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|          |                                                           7 + 4*x                7 + 4*x                        7 + 4*x                                    2       |   72*x *(-5 + 3*x)*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|     \                                       7 + 4*x        / |                                                           7 + 4*x                 7 + 4*x                        2       |     \                                       7 + 4*x        / |                                                           7 + 4*x                7 + 4*x                        7 + 4*x                                    2       |   12*x*(-5 + 3*x)*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|   4*(-5 + 3*x)*|3*x  - ------------|*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|   6*x *(-5 + 3*x)*|3*x  - ------------|*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|   48*x *(-5 + 3*x)*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------||
      /  9 + 2*x   |      \                                       7 + 4*x        /      \                                                                                                                                                   (7 + 4*x)        /     \                                                                                                                           (7 + 4*x)                                                                                                            (7 + 4*x)                        (7 + 4*x)               (7 + 4*x)        /      \                                                                                                                                                   (7 + 4*x)        /      \                                       7 + 4*x        /   \                                       7 + 4*x        /  \         7 + 4*x   /          \                                       7 + 4*x        /     \                                       7 + 4*x        /                            \                                                                                                                                                   (7 + 4*x)        /         \                                       7 + 4*x        /       \         7 + 4*x   / \                                       7 + 4*x        /      \                                       7 + 4*x        /          \                                                                                                                                                   (7 + 4*x)        /                    \                                       7 + 4*x        /                                                              \                                                                                                         (7 + 4*x)        /                                                              \                                                                                                                                                   (7 + 4*x)        /                   \                                       7 + 4*x        /                \         7 + 4*x   / \                                       7 + 4*x        /                   \         7 + 4*x   / \                                       7 + 4*x        /                    \                                       7 + 4*x        /|
-7*  /   -------- *|- ------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------- - ------------------------------------------------------------------------------- - --------------------------------------------------------------- - ----------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------- + --------------------------------------------------------------------------------- + ------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------|
   \/    7 + 4*x   |                            -5 + 3*x                                                                                                              7 + 4*x                                                                                                                                                                                                                                               -5 + 3*x                                                                                                                                                                                                                                               -5 + 3*x                                                                                                             7 + 4*x                                                                         2                                                                        3                                                            /       3\                                                                                                                        3                                                                                                                                  2                                                                         3                                                                     /       3\                                                                                                                3                                                                                                                              2                                                                                                                              /       3\                                                                                                                                                                                                     /       3\                                                                                                                                                3                                                                                 /       3\                                                                                         2                                                                                  /       3\                          |
                   |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          /       3\                                                                  9 + 2*x                                                   (7 + 4*x)*\9 + 2*x /                                                                                                                 9 + 2*x                                                                                                                         /       3\                                                                   9 + 2*x                                                           (-5 + 3*x)*\9 + 2*x /                                                                                                         9 + 2*x                                                                                                                     /       3\                                                                                                                    (-5 + 3*x)*\9 + 2*x /                                                                                                                                                                                          (-5 + 3*x)*\9 + 2*x /                                                                                                                                         9 + 2*x                                                                        (7 + 4*x)*\9 + 2*x /                                                                               /       3\                                                                         (7 + 4*x)*\9 + 2*x /                          |
                   \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          \9 + 2*x /                                                                                                                                                                                                                                                                                                                                                                                                 \9 + 2*x /                                                                                                                                                                                                                                                                                                                                                                                               \9 + 2*x /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \9 + 2*x /                                                                                                                       /
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             9 + 2*x
−72x3+94x+7(−72x4(3x−5)(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)(2x3+9)2+6x2(3x−5)(3x2−2(2x3+9)4x+7)(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)(2x3+9)2+48x2(3x−5)(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)(4x+7)(2x3+9)−108x2(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)2x3+9+24x2(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)2x3+9+12x2(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)2(2x3+9)2+12x(3x−5)(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)2x3+9−4(3x−5)(3x2−2(2x3+9)4x+7)(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)(4x+7)(2x3+9)+12(3x2−2(2x3+9)4x+7)(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)2x3+9−2(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)2x3+9−(3x2−2(2x3+9)4x+7)(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)2(2x3+9)2+72(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)4x+7−16(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)4x+7−8(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)2(4x+7)(2x3+9)−108(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)3x−5+36(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−5−6(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+18(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)2(3x−5)(2x3+9)−2(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)(2x3+9)−2(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)(2x3+9))2x3+9- \frac{7 \sqrt{\frac{2 x^{3} + 9}{4 x + 7}} \left(- \frac{72 x^{4} \left(3 x - 5\right) \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)}{\left(2 x^{3} + 9\right)^{2}} + \frac{6 x^{2} \left(3 x - 5\right) \left(3 x^{2} - \frac{2 \left(2 x^{3} + 9\right)}{4 x + 7}\right) \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)}{\left(2 x^{3} + 9\right)^{2}} + \frac{48 x^{2} \left(3 x - 5\right) \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)}{\left(4 x + 7\right) \left(2 x^{3} + 9\right)} - \frac{108 x^{2} \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)}{2 x^{3} + 9} + \frac{24 x^{2} \left(54 x^{3} - \frac{6 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} + 36 x^{2} \left(3 x - 5\right) + 3 x \left(3 x - 5\right)^{2} + \frac{8 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} - \frac{12 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - \frac{6 \left(3 x - 5\right) \left(4 x^{3} + x^{2} \left(3 x - 5\right) + 18\right)}{4 x + 7} + 243\right)}{2 x^{3} + 9} + \frac{12 x^{2} \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)^{2}}{\left(2 x^{3} + 9\right)^{2}} + \frac{12 x \left(3 x - 5\right) \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)}{2 x^{3} + 9} - \frac{4 \left(3 x - 5\right) \left(3 x^{2} - \frac{2 \left(2 x^{3} + 9\right)}{4 x + 7}\right) \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)}{\left(4 x + 7\right) \left(2 x^{3} + 9\right)} + \frac{12 \left(3 x^{2} - \frac{2 \left(2 x^{3} + 9\right)}{4 x + 7}\right) \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)}{2 x^{3} + 9} - \frac{2 \left(3 x^{2} - \frac{2 \left(2 x^{3} + 9\right)}{4 x + 7}\right) \left(54 x^{3} - \frac{6 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} + 36 x^{2} \left(3 x - 5\right) + 3 x \left(3 x - 5\right)^{2} + \frac{8 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} - \frac{12 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - \frac{6 \left(3 x - 5\right) \left(4 x^{3} + x^{2} \left(3 x - 5\right) + 18\right)}{4 x + 7} + 243\right)}{2 x^{3} + 9} - \frac{\left(3 x^{2} - \frac{2 \left(2 x^{3} + 9\right)}{4 x + 7}\right) \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)^{2}}{\left(2 x^{3} + 9\right)^{2}} + \frac{72 \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)}{4 x + 7} - \frac{16 \left(54 x^{3} - \frac{6 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} + 36 x^{2} \left(3 x - 5\right) + 3 x \left(3 x - 5\right)^{2} + \frac{8 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} - \frac{12 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - \frac{6 \left(3 x - 5\right) \left(4 x^{3} + x^{2} \left(3 x - 5\right) + 18\right)}{4 x + 7} + 243\right)}{4 x + 7} - \frac{8 \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)^{2}}{\left(4 x + 7\right) \left(2 x^{3} + 9\right)} - \frac{108 \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)}{3 x - 5} + \frac{36 \left(54 x^{3} - \frac{6 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} + 36 x^{2} \left(3 x - 5\right) + 3 x \left(3 x - 5\right)^{2} + \frac{8 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} - \frac{12 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - \frac{6 \left(3 x - 5\right) \left(4 x^{3} + x^{2} \left(3 x - 5\right) + 18\right)}{4 x + 7} + 243\right)}{3 x - 5} - \frac{6 \left(108 x^{3} + \frac{32 x^{2} \left(3 x - 5\right)^{3}}{\left(4 x + 7\right)^{2}} - \frac{48 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} + 162 x^{2} \left(3 x - 5\right) - \frac{4 x \left(3 x - 5\right)^{3}}{4 x + 7} + 36 x \left(3 x - 5\right)^{2} + \left(3 x - 5\right)^{3} - \frac{32 \left(3 x - 5\right)^{3} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{3}} + \frac{64 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} + \frac{16 \left(3 x - 5\right)^{2} \left(4 x^{3} + x^{2} \left(3 x - 5\right) + 18\right)}{\left(4 x + 7\right)^{2}} - \frac{36 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - \frac{8 \left(3 x - 5\right) \left(18 x^{3} + 12 x^{2} \left(3 x - 5\right) + x \left(3 x - 5\right)^{2} + 81\right)}{4 x + 7} + 486\right)}{3 x - 5} + \frac{18 \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)^{2}}{\left(3 x - 5\right) \left(2 x^{3} + 9\right)} - \frac{2 \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right) \left(54 x^{3} - \frac{12 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} + 36 x^{2} \left(3 x - 5\right) + 3 x \left(3 x - 5\right)^{2} + \frac{8 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} - \frac{24 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 243\right)}{\left(3 x - 5\right) \left(2 x^{3} + 9\right)} - \frac{2 \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right) \left(54 x^{3} - \frac{6 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} + 36 x^{2} \left(3 x - 5\right) + 3 x \left(3 x - 5\right)^{2} + \frac{8 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} - \frac{12 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - \frac{6 \left(3 x - 5\right) \left(4 x^{3} + x^{2} \left(3 x - 5\right) + 18\right)}{4 x + 7} + 243\right)}{\left(3 x - 5\right) \left(2 x^{3} + 9\right)}\right)}{2 x^{3} + 9}
Simplificar
Gráfico
Derivada de y=7sqrt((3x-5)^4(2x^3+9)/(4x+7))
    © Sr Examen – Калькулятор