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

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

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

Gráfico:

interior superior

Definida a trozos:

Solución

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

  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}}

  4. Simplificamos:

    216x5−39x4−850x3+1011x2+594x−23402x3+94x+7(16x2+56x+49)\frac{216 x^{5} - 39 x^{4} - 850 x^{3} + 1011 x^{2} + 594 x - 2340}{\sqrt{\frac{2 x^{3} + 9}{4 x + 7}} \left(16 x^{2} + 56 x + 49\right)}

Respuesta:

216x5−39x4−850x3+1011x2+594x−23402x3+94x+7(16x2+56x+49)\frac{216 x^{5} - 39 x^{4} - 850 x^{3} + 1011 x^{2} + 594 x - 2340}{\sqrt{\frac{2 x^{3} + 9}{4 x + 7}} \left(16 x^{2} + 56 x + 49\right)}

Gráfica
02468-8-6-4-2-1010-1000010000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
     _______________________                                                                                 
    /          4 /   3    \            /   2          4               3 /   3    \              4 /   3    \\
   /  (3*x - 5) *\2*x  + 9/            |6*x *(3*x - 5)  + 12*(3*x - 5) *\2*x  + 9/   2*(3*x - 5) *\2*x  + 9/|
  /   --------------------- *(4*x + 7)*|------------------------------------------ - -----------------------|
\/           4*x + 7                   |               2*(4*x + 7)                                   2      |
                                       \                                                    (4*x + 7)       /
-------------------------------------------------------------------------------------------------------------
                                            /   3    \          4                                            
                                            \2*x  + 9/*(3*x - 5)
(3x−5)4(2x3+9)4x+7(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{\sqrt{\frac{\left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)}{4 x + 7}} \left(4 x + 7\right) \left(- \frac{2 \left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} + \frac{6 x^{2} \left(3 x - 5\right)^{4} + 12 \left(3 x - 5\right)^{3} \left(2 x^{3} + 9\right)}{2 \left(4 x + 7\right)}\right)}{\left(3 x - 5\right)^{4} \left(2 x^{3} + 9\right)}
Simplificar
Segunda derivada [src] 
                /                                                    /                                             /       3\\ /                                            /       3\\                                                                                /                                             /       3\\                                               /                                             /       3\\\
     __________ |                                                    |          3      2              2*(-5 + 3*x)*\9 + 2*x /| |         3      2              2*(-5 + 3*x)*\9 + 2*x /|                                                                                |          3      2              2*(-5 + 3*x)*\9 + 2*x /|                                  2            |          3      2              2*(-5 + 3*x)*\9 + 2*x /||
    /        3  |                                                    |-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|       2           2                 /        3    2           \   4*(-5 + 3*x)*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|                2 /       3\   6*x *(-5 + 3*x)*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------||
   /  9 + 2*x   |           3                 2       2              \                                        7 + 4*x        / \                                       7 + 4*x        /   12*x *(-5 + 3*x)    12*(-5 + 3*x)*\18 + 4*x  + x *(-5 + 3*x)/                \                                        7 + 4*x        /   16*(-5 + 3*x) *\9 + 2*x /                   \                                        7 + 4*x        /|
  /   -------- *|-162 - 36*x  + 6*x*(-5 + 3*x)  + 36*x *(-5 + 3*x) - ------------------------------------------------------------------------------------------------------------------ - ----------------- - ----------------------------------------- - ---------------------------------------------------------------------- + ------------------------- + -------------------------------------------------------------------------|
\/    7 + 4*x   |                                                                                                                3                                                             7 + 4*x                         7 + 4*x                                                   7 + 4*x                                                    2                                                  3                                |
                \                                                                                                         9 + 2*x                                                                                                                                                                                                          (7 + 4*x)                                            9 + 2*x                                 /
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                                                                                                                                                                                                                 9 + 2*x
2x3+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)(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)2x3+9)2x3+9\frac{\sqrt{\frac{2 x^{3} + 9}{4 x + 7}} \left(- 36 x^{3} - \frac{12 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} + 36 x^{2} \left(3 x - 5\right) + \frac{6 x^{2} \left(3 x - 5\right) \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{2 x^{3} + 9} + 6 x \left(3 x - 5\right)^{2} + \frac{16 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} - \frac{12 \left(3 x - 5\right) \left(4 x^{3} + x^{2} \left(3 x - 5\right) + 18\right)}{4 x + 7} - \frac{4 \left(3 x - 5\right) \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{4 x + 7} - 162 - \frac{\left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right) \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)}{2 x^{3} + 9}\right)}{2 x^{3} + 9}
Simplificar
Tercera derivada [src] 
                /                                                                     /                                                                2 /       3\      2           2                /        3    2           \                 /       3\\     /                                                                                  2 /       3\       2           3                2 /        3    2           \                 3                /         3               2       2           \                3 /       3\                 /       3\       2           2\      /                                                                2 /       3\      2           2                /        3    2           \                 /       3\\                                                                                                                                       /         /       3\\ /                                                                2 /       3\      2           2                /        3    2           \                 /       3\\                                                                                              /                                                                2 /       3\      2           2                /        3    2           \                 /       3\\                                                                                                                                                                                                                                                                                                                                                    /                                             /       3\\ /                                                                 /       3\       2           2               2 /       3\\     /                                            /       3\\ /                                                                2 /       3\      2           2                /        3    2           \                 /       3\\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \
                |      /                                             /       3\\      |           3       2                            2   8*(-5 + 3*x) *\9 + 2*x /   6*x *(-5 + 3*x)    6*(-5 + 3*x)*\18 + 4*x  + x *(-5 + 3*x)/   12*(-5 + 3*x)*\9 + 2*x /|     |                 3        3        2                             2   64*(-5 + 3*x) *\9 + 2*x /   32*x *(-5 + 3*x)    16*(-5 + 3*x) *\18 + 4*x  + x *(-5 + 3*x)/   4*x*(-5 + 3*x)    8*(-5 + 3*x)*\81 + 18*x  + x*(-5 + 3*x)  + 12*x *(-5 + 3*x)/   32*(-5 + 3*x) *\9 + 2*x /   36*(-5 + 3*x)*\9 + 2*x /   48*x *(-5 + 3*x) |      |           3       2                            2   8*(-5 + 3*x) *\9 + 2*x /   6*x *(-5 + 3*x)    6*(-5 + 3*x)*\18 + 4*x  + x *(-5 + 3*x)/   12*(-5 + 3*x)*\9 + 2*x /|      /                                             /       3\\          /                                             /       3\\     |   2   2*\9 + 2*x /| |           3       2                            2   8*(-5 + 3*x) *\9 + 2*x /   6*x *(-5 + 3*x)    6*(-5 + 3*x)*\18 + 4*x  + x *(-5 + 3*x)/   12*(-5 + 3*x)*\9 + 2*x /|      /         /       3\\ /                                             /       3\\       2 |           3       2                            2   8*(-5 + 3*x) *\9 + 2*x /   6*x *(-5 + 3*x)    6*(-5 + 3*x)*\18 + 4*x  + x *(-5 + 3*x)/   12*(-5 + 3*x)*\9 + 2*x /|   /         /       3\\ /                                             /       3\\ /                                            /       3\\                    /                                             /       3\\     /                                             /       3\\ /                                            /       3\\     |          3      2              2*(-5 + 3*x)*\9 + 2*x /| |          3                 2       2              24*(-5 + 3*x)*\9 + 2*x /   12*x *(-5 + 3*x)    8*(-5 + 3*x) *\9 + 2*x /|     |         3      2              2*(-5 + 3*x)*\9 + 2*x /| |           3       2                            2   8*(-5 + 3*x) *\9 + 2*x /   6*x *(-5 + 3*x)    6*(-5 + 3*x)*\18 + 4*x  + x *(-5 + 3*x)/   12*(-5 + 3*x)*\9 + 2*x /|                   /                                             /       3\\         /                                             /       3\\ /                                            /       3\\      /                                             /       3\\ /                                            /       3\\                /         /       3\\ /                                             /       3\\                   /         /       3\\ /                                             /       3\\                    /                                             /       3\\|
     __________ |      |          3      2              2*(-5 + 3*x)*\9 + 2*x /|   16*|-243 - 54*x  - 36*x *(-5 + 3*x) - 3*x*(-5 + 3*x)  - ------------------------ + ---------------- + ---------------------------------------- + ------------------------|   6*|-486 - (-5 + 3*x)  - 108*x  - 162*x *(-5 + 3*x) - 36*x*(-5 + 3*x)  - ------------------------- - ----------------- - ------------------------------------------ + --------------- + ------------------------------------------------------------ + ------------------------- + ------------------------ + -----------------|   36*|-243 - 54*x  - 36*x *(-5 + 3*x) - 3*x*(-5 + 3*x)  - ------------------------ + ---------------- + ---------------------------------------- + ------------------------|      |          3      2              2*(-5 + 3*x)*\9 + 2*x /|        2 |          3      2              2*(-5 + 3*x)*\9 + 2*x /|   2*|3*x  - ------------|*|-243 - 54*x  - 36*x *(-5 + 3*x) - 3*x*(-5 + 3*x)  - ------------------------ + ---------------- + ---------------------------------------- + ------------------------|      |   2   2*\9 + 2*x /| |          3      2              2*(-5 + 3*x)*\9 + 2*x /|   24*x *|-243 - 54*x  - 36*x *(-5 + 3*x) - 3*x*(-5 + 3*x)  - ------------------------ + ---------------- + ---------------------------------------- + ------------------------|   |   2   2*\9 + 2*x /| |          3      2              2*(-5 + 3*x)*\9 + 2*x /| |         3      2              2*(-5 + 3*x)*\9 + 2*x /|       4            |          3      2              2*(-5 + 3*x)*\9 + 2*x /|     |          3      2              2*(-5 + 3*x)*\9 + 2*x /| |         3      2              2*(-5 + 3*x)*\9 + 2*x /|   2*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|*|243 + 54*x  + 3*x*(-5 + 3*x)  + 36*x *(-5 + 3*x) - ------------------------ - ----------------- + ------------------------|   2*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|*|-243 - 54*x  - 36*x *(-5 + 3*x) - 3*x*(-5 + 3*x)  - ------------------------ + ---------------- + ---------------------------------------- + ------------------------|                   |          3      2              2*(-5 + 3*x)*\9 + 2*x /|       2 |          3      2              2*(-5 + 3*x)*\9 + 2*x /| |         3      2              2*(-5 + 3*x)*\9 + 2*x /|      |          3      2              2*(-5 + 3*x)*\9 + 2*x /| |         3      2              2*(-5 + 3*x)*\9 + 2*x /|                |   2   2*\9 + 2*x /| |          3      2              2*(-5 + 3*x)*\9 + 2*x /|      2            |   2   2*\9 + 2*x /| |          3      2              2*(-5 + 3*x)*\9 + 2*x /|       2            |          3      2              2*(-5 + 3*x)*\9 + 2*x /||
    /        3  |  108*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|      |                                                                    2              7 + 4*x                        7 + 4*x                            7 + 4*x         |     |                                                                                      2                       2                               2                       7 + 4*x                                 7 + 4*x                                               3                  7 + 4*x                 7 + 4*x     |      |                                                                    2              7 + 4*x                        7 + 4*x                            7 + 4*x         |   72*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|   108*x *|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|     \         7 + 4*x   / |                                                                    2              7 + 4*x                        7 + 4*x                            7 + 4*x         |   12*|3*x  - ------------|*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|         |                                                                    2              7 + 4*x                        7 + 4*x                            7 + 4*x         |   |3*x  - ------------|*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|   72*x *(-5 + 3*x)*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|   8*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|     \                                        7 + 4*x        / |                                                           7 + 4*x                 7 + 4*x                        2       |     \                                       7 + 4*x        / |                                                                    2              7 + 4*x                        7 + 4*x                            7 + 4*x         |   12*x*(-5 + 3*x)*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|   12*x *|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|   18*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|*|54 + 12*x  + 3*x *(-5 + 3*x) - -----------------------|   4*(-5 + 3*x)*|3*x  - ------------|*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|   6*x *(-5 + 3*x)*|3*x  - ------------|*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------|   48*x *(-5 + 3*x)*|-54 - 12*x  - 3*x *(-5 + 3*x) + -----------------------||
   /  9 + 2*x   |      \                                        7 + 4*x        /      \                                                           (7 + 4*x)                                                                                                 /     \                                                                             (7 + 4*x)               (7 + 4*x)                       (7 + 4*x)                                                                                                             (7 + 4*x)                                                       /      \                                                           (7 + 4*x)                                                                                                 /      \                                        7 + 4*x        /          \                                        7 + 4*x        /                           \                                                           (7 + 4*x)                                                                                                 /      \         7 + 4*x   / \                                        7 + 4*x        /         \                                                           (7 + 4*x)                                                                                                 /   \         7 + 4*x   / \                                        7 + 4*x        / \                                       7 + 4*x        /                    \                                        7 + 4*x        /     \                                        7 + 4*x        / \                                       7 + 4*x        /                                                               \                                                                                                         (7 + 4*x)        /                                                              \                                                           (7 + 4*x)                                                                                                 /                   \                                        7 + 4*x        /         \                                        7 + 4*x        / \                                       7 + 4*x        /      \                                        7 + 4*x        / \                                       7 + 4*x        /                \         7 + 4*x   / \                                        7 + 4*x        /                   \         7 + 4*x   / \                                        7 + 4*x        /                    \                                        7 + 4*x        /|
  /   -------- *|- ------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------ - ---------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------|
\/    7 + 4*x   |                             -5 + 3*x                                                                                                              7 + 4*x                                                                                                                                                                                                                                                 -5 + 3*x                                                                                                                                                                                                                                               -5 + 3*x                                                                                                              7 + 4*x                                                                 3                                                                                                                                  3                                                                                                                                          3                                                                                                                                  3                                                                                                                                                             2                                                                                                           2                                                                                             /       3\                                                                                                                                               /       3\                                                                                                                                                                                                      /       3\                                                                                                                                                  3                                                                                                   2                                                                                                                     /       3\                                                                                                 /       3\                                                                                           2                                                                                  /       3\                           |
                |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         9 + 2*x                                                                                                                            9 + 2*x                                                                                                                                    9 + 2*x                                                                                                                            9 + 2*x                                                                                                                                                    /       3\                                                                                                  /       3\                                                                                    (7 + 4*x)*\9 + 2*x /                                                                                                                                    (-5 + 3*x)*\9 + 2*x /                                                                                                                                                                                           (-5 + 3*x)*\9 + 2*x /                                                                                                                                           9 + 2*x                                                                                          /       3\                                                                                                           (-5 + 3*x)*\9 + 2*x /                                                                                       (7 + 4*x)*\9 + 2*x /                                                                                 /       3\                                                                         (7 + 4*x)*\9 + 2*x /                           |
                \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     \9 + 2*x /                                                                                                  \9 + 2*x /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \9 + 2*x /                                                                                                                                                                                                                                                                                                                            \9 + 2*x /                                                                                                                        /
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2x3+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)(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)(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)(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)(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)(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)(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)(12x3+3x2(3x−5)−2(3x−5)(2x3+9)4x+7+54)(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{\sqrt{\frac{2 x^{3} + 9}{4 x + 7}} \left(- \frac{72 x^{4} \left(3 x - 5\right) \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{\left(2 x^{3} + 9\right)^{2}} + \frac{6 x^{2} \left(3 x - 5\right) \left(3 x^{2} - \frac{2 \left(2 x^{3} + 9\right)}{4 x + 7}\right) \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{\left(2 x^{3} + 9\right)^{2}} + \frac{48 x^{2} \left(3 x - 5\right) \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{\left(4 x + 7\right) \left(2 x^{3} + 9\right)} - \frac{108 x^{2} \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{2 x^{3} + 9} + \frac{24 x^{2} \left(- 54 x^{3} + \frac{6 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} - 36 x^{2} \left(3 x - 5\right) - 3 x \left(3 x - 5\right)^{2} - \frac{8 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} + \frac{12 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + \frac{6 \left(3 x - 5\right) \left(4 x^{3} + x^{2} \left(3 x - 5\right) + 18\right)}{4 x + 7} - 243\right)}{2 x^{3} + 9} + \frac{12 x^{2} \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right) \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)}{\left(2 x^{3} + 9\right)^{2}} + \frac{12 x \left(3 x - 5\right) \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{2 x^{3} + 9} - \frac{4 \left(3 x - 5\right) \left(3 x^{2} - \frac{2 \left(2 x^{3} + 9\right)}{4 x + 7}\right) \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{\left(4 x + 7\right) \left(2 x^{3} + 9\right)} + \frac{12 \left(3 x^{2} - \frac{2 \left(2 x^{3} + 9\right)}{4 x + 7}\right) \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{2 x^{3} + 9} - \frac{2 \left(3 x^{2} - \frac{2 \left(2 x^{3} + 9\right)}{4 x + 7}\right) \left(- 54 x^{3} + \frac{6 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} - 36 x^{2} \left(3 x - 5\right) - 3 x \left(3 x - 5\right)^{2} - \frac{8 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} + \frac{12 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + \frac{6 \left(3 x - 5\right) \left(4 x^{3} + x^{2} \left(3 x - 5\right) + 18\right)}{4 x + 7} - 243\right)}{2 x^{3} + 9} - \frac{\left(3 x^{2} - \frac{2 \left(2 x^{3} + 9\right)}{4 x + 7}\right) \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right) \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)}{\left(2 x^{3} + 9\right)^{2}} + \frac{72 \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{4 x + 7} - \frac{16 \left(- 54 x^{3} + \frac{6 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} - 36 x^{2} \left(3 x - 5\right) - 3 x \left(3 x - 5\right)^{2} - \frac{8 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} + \frac{12 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + \frac{6 \left(3 x - 5\right) \left(4 x^{3} + x^{2} \left(3 x - 5\right) + 18\right)}{4 x + 7} - 243\right)}{4 x + 7} - \frac{8 \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right) \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)}{\left(4 x + 7\right) \left(2 x^{3} + 9\right)} - \frac{108 \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right)}{3 x - 5} + \frac{36 \left(- 54 x^{3} + \frac{6 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} - 36 x^{2} \left(3 x - 5\right) - 3 x \left(3 x - 5\right)^{2} - \frac{8 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} + \frac{12 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + \frac{6 \left(3 x - 5\right) \left(4 x^{3} + x^{2} \left(3 x - 5\right) + 18\right)}{4 x + 7} - 243\right)}{3 x - 5} - \frac{6 \left(- 108 x^{3} - \frac{32 x^{2} \left(3 x - 5\right)^{3}}{\left(4 x + 7\right)^{2}} + \frac{48 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} - 162 x^{2} \left(3 x - 5\right) + \frac{4 x \left(3 x - 5\right)^{3}}{4 x + 7} - 36 x \left(3 x - 5\right)^{2} - \left(3 x - 5\right)^{3} + \frac{32 \left(3 x - 5\right)^{3} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{3}} - \frac{64 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} - \frac{16 \left(3 x - 5\right)^{2} \left(4 x^{3} + x^{2} \left(3 x - 5\right) + 18\right)}{\left(4 x + 7\right)^{2}} + \frac{36 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + \frac{8 \left(3 x - 5\right) \left(18 x^{3} + 12 x^{2} \left(3 x - 5\right) + x \left(3 x - 5\right)^{2} + 81\right)}{4 x + 7} - 486\right)}{3 x - 5} + \frac{18 \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right) \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right)}{\left(3 x - 5\right) \left(2 x^{3} + 9\right)} - \frac{2 \left(- 12 x^{3} - 3 x^{2} \left(3 x - 5\right) + \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} - 54\right) \left(54 x^{3} - \frac{12 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} + 36 x^{2} \left(3 x - 5\right) + 3 x \left(3 x - 5\right)^{2} + \frac{8 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} - \frac{24 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 243\right)}{\left(3 x - 5\right) \left(2 x^{3} + 9\right)} - \frac{2 \left(12 x^{3} + 3 x^{2} \left(3 x - 5\right) - \frac{2 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + 54\right) \left(- 54 x^{3} + \frac{6 x^{2} \left(3 x - 5\right)^{2}}{4 x + 7} - 36 x^{2} \left(3 x - 5\right) - 3 x \left(3 x - 5\right)^{2} - \frac{8 \left(3 x - 5\right)^{2} \left(2 x^{3} + 9\right)}{\left(4 x + 7\right)^{2}} + \frac{12 \left(3 x - 5\right) \left(2 x^{3} + 9\right)}{4 x + 7} + \frac{6 \left(3 x - 5\right) \left(4 x^{3} + x^{2} \left(3 x - 5\right) + 18\right)}{4 x + 7} - 243\right)}{\left(3 x - 5\right) \left(2 x^{3} + 9\right)}\right)}{2 x^{3} + 9}
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Gráfico
Derivada de y=sqrt((3x-5)^4(2x^3+9)/(4x+7))
    © Sr Examen – Калькулятор