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x*(x-1)*(x-2)*(x-3)*(x-4)*(x-5)*(x-6)*(x-8)*(x-9)*(x-10)

Derivada de x*(x-1)*(x-2)*(x-3)*(x-4)*(x-5)*(x-6)*(x-8)*(x-9)*(x-10)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src]
x*(x - 1)*(x - 2)*(x - 3)*(x - 4)*(x - 5)*(x - 6)*(x - 8)*(x - 9)*(x - 10)
x(x1)(x2)(x3)(x4)(x5)(x6)(x8)(x9)(x10)x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) \left(x - 5\right) \left(x - 6\right) \left(x - 8\right) \left(x - 9\right) \left(x - 10\right)
((((((((x*(x - 1))*(x - 2))*(x - 3))*(x - 4))*(x - 5))*(x - 6))*(x - 8))*(x - 9))*(x - 10)
Solución detallada
  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)=x(x1)(x2)(x3)(x4)(x5)(x6)(x8)(x9)f{\left(x \right)} = x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) \left(x - 5\right) \left(x - 6\right) \left(x - 8\right) \left(x - 9\right); calculamos 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)=x(x1)(x2)(x3)(x4)(x5)(x6)(x8)f{\left(x \right)} = x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) \left(x - 5\right) \left(x - 6\right) \left(x - 8\right); calculamos 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)=x(x1)(x2)(x3)(x4)(x5)(x6)f{\left(x \right)} = x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) \left(x - 5\right) \left(x - 6\right); calculamos 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)=x(x1)(x2)(x3)(x4)(x5)f{\left(x \right)} = x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) \left(x - 5\right); calculamos 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)=x(x1)(x2)(x3)(x4)f{\left(x \right)} = x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right); calculamos 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)=x(x1)(x2)(x3)f{\left(x \right)} = x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right); calculamos 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)=x(x1)(x2)f{\left(x \right)} = x \left(x - 1\right) \left(x - 2\right); calculamos 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)=x(x1)f{\left(x \right)} = x \left(x - 1\right); calculamos 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)=xf{\left(x \right)} = x; calculamos ddxf(x)\frac{d}{d x} f{\left(x \right)}:

                    1. Según el principio, aplicamos: xx tenemos 11

                    g(x)=x1g{\left(x \right)} = x - 1; calculamos ddxg(x)\frac{d}{d x} g{\left(x \right)}:

                    1. diferenciamos x1x - 1 miembro por miembro:

                      1. Según el principio, aplicamos: xx tenemos 11

                      2. La derivada de una constante 1-1 es igual a cero.

                      Como resultado de: 11

                    Como resultado de: 2x12 x - 1

                  g(x)=x2g{\left(x \right)} = x - 2; calculamos ddxg(x)\frac{d}{d x} g{\left(x \right)}:

                  1. diferenciamos x2x - 2 miembro por miembro:

                    1. Según el principio, aplicamos: xx tenemos 11

                    2. La derivada de una constante 2-2 es igual a cero.

                    Como resultado de: 11

                  Como resultado de: x(x1)+(x2)(2x1)x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)

                g(x)=x3g{\left(x \right)} = x - 3; calculamos ddxg(x)\frac{d}{d x} g{\left(x \right)}:

                1. diferenciamos x3x - 3 miembro por miembro:

                  1. Según el principio, aplicamos: xx tenemos 11

                  2. La derivada de una constante 3-3 es igual a cero.

                  Como resultado de: 11

                Como resultado de: x(x1)(x2)+(x3)(x(x1)+(x2)(2x1))x \left(x - 1\right) \left(x - 2\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)

              g(x)=x4g{\left(x \right)} = x - 4; calculamos ddxg(x)\frac{d}{d x} g{\left(x \right)}:

              1. diferenciamos x4x - 4 miembro por miembro:

                1. Según el principio, aplicamos: xx tenemos 11

                2. La derivada de una constante 4-4 es igual a cero.

                Como resultado de: 11

              Como resultado de: x(x1)(x2)(x3)+(x4)(x(x1)(x2)+(x3)(x(x1)+(x2)(2x1)))x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) + \left(x - 4\right) \left(x \left(x - 1\right) \left(x - 2\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right)

            g(x)=x5g{\left(x \right)} = x - 5; calculamos ddxg(x)\frac{d}{d x} g{\left(x \right)}:

            1. diferenciamos x5x - 5 miembro por miembro:

              1. Según el principio, aplicamos: xx tenemos 11

              2. La derivada de una constante 5-5 es igual a cero.

              Como resultado de: 11

            Como resultado de: x(x1)(x2)(x3)(x4)+(x5)(x(x1)(x2)(x3)+(x4)(x(x1)(x2)+(x3)(x(x1)+(x2)(2x1))))x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) + \left(x - 5\right) \left(x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) + \left(x - 4\right) \left(x \left(x - 1\right) \left(x - 2\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right)\right)

          g(x)=x6g{\left(x \right)} = x - 6; calculamos ddxg(x)\frac{d}{d x} g{\left(x \right)}:

          1. diferenciamos x6x - 6 miembro por miembro:

            1. Según el principio, aplicamos: xx tenemos 11

            2. La derivada de una constante 6-6 es igual a cero.

            Como resultado de: 11

          Como resultado de: x(x1)(x2)(x3)(x4)(x5)+(x6)(x(x1)(x2)(x3)(x4)+(x5)(x(x1)(x2)(x3)+(x4)(x(x1)(x2)+(x3)(x(x1)+(x2)(2x1)))))x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) \left(x - 5\right) + \left(x - 6\right) \left(x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) + \left(x - 5\right) \left(x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) + \left(x - 4\right) \left(x \left(x - 1\right) \left(x - 2\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right)\right)\right)

        g(x)=x8g{\left(x \right)} = x - 8; calculamos ddxg(x)\frac{d}{d x} g{\left(x \right)}:

        1. diferenciamos x8x - 8 miembro por miembro:

          1. Según el principio, aplicamos: xx tenemos 11

          2. La derivada de una constante 8-8 es igual a cero.

          Como resultado de: 11

        Como resultado de: x(x1)(x2)(x3)(x4)(x5)(x6)+(x8)(x(x1)(x2)(x3)(x4)(x5)+(x6)(x(x1)(x2)(x3)(x4)+(x5)(x(x1)(x2)(x3)+(x4)(x(x1)(x2)+(x3)(x(x1)+(x2)(2x1))))))x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) \left(x - 5\right) \left(x - 6\right) + \left(x - 8\right) \left(x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) \left(x - 5\right) + \left(x - 6\right) \left(x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) + \left(x - 5\right) \left(x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) + \left(x - 4\right) \left(x \left(x - 1\right) \left(x - 2\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right)\right)\right)\right)

      g(x)=x9g{\left(x \right)} = x - 9; calculamos ddxg(x)\frac{d}{d x} g{\left(x \right)}:

      1. diferenciamos x9x - 9 miembro por miembro:

        1. Según el principio, aplicamos: xx tenemos 11

        2. La derivada de una constante 9-9 es igual a cero.

        Como resultado de: 11

      Como resultado de: x(x1)(x2)(x3)(x4)(x5)(x6)(x8)+(x9)(x(x1)(x2)(x3)(x4)(x5)(x6)+(x8)(x(x1)(x2)(x3)(x4)(x5)+(x6)(x(x1)(x2)(x3)(x4)+(x5)(x(x1)(x2)(x3)+(x4)(x(x1)(x2)+(x3)(x(x1)+(x2)(2x1)))))))x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) \left(x - 5\right) \left(x - 6\right) \left(x - 8\right) + \left(x - 9\right) \left(x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) \left(x - 5\right) \left(x - 6\right) + \left(x - 8\right) \left(x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) \left(x - 5\right) + \left(x - 6\right) \left(x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) + \left(x - 5\right) \left(x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) + \left(x - 4\right) \left(x \left(x - 1\right) \left(x - 2\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right)\right)\right)\right)\right)

    g(x)=x10g{\left(x \right)} = x - 10; calculamos ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. diferenciamos x10x - 10 miembro por miembro:

      1. Según el principio, aplicamos: xx tenemos 11

      2. La derivada de una constante 10-10 es igual a cero.

      Como resultado de: 11

    Como resultado de: x(x1)(x2)(x3)(x4)(x5)(x6)(x8)(x9)+(x10)(x(x1)(x2)(x3)(x4)(x5)(x6)(x8)+(x9)(x(x1)(x2)(x3)(x4)(x5)(x6)+(x8)(x(x1)(x2)(x3)(x4)(x5)+(x6)(x(x1)(x2)(x3)(x4)+(x5)(x(x1)(x2)(x3)+(x4)(x(x1)(x2)+(x3)(x(x1)+(x2)(2x1))))))))x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) \left(x - 5\right) \left(x - 6\right) \left(x - 8\right) \left(x - 9\right) + \left(x - 10\right) \left(x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) \left(x - 5\right) \left(x - 6\right) \left(x - 8\right) + \left(x - 9\right) \left(x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) \left(x - 5\right) \left(x - 6\right) + \left(x - 8\right) \left(x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) \left(x - 5\right) + \left(x - 6\right) \left(x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) + \left(x - 5\right) \left(x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) + \left(x - 4\right) \left(x \left(x - 1\right) \left(x - 2\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right)\right)\right)\right)\right)\right)

  2. Simplificamos:

    10x9432x8+7872x778834x6+473634x51747410x4+3882224x34846824x2+2888640x51840010 x^{9} - 432 x^{8} + 7872 x^{7} - 78834 x^{6} + 473634 x^{5} - 1747410 x^{4} + 3882224 x^{3} - 4846824 x^{2} + 2888640 x - 518400


Respuesta:

10x9432x8+7872x778834x6+473634x51747410x4+3882224x34846824x2+2888640x51840010 x^{9} - 432 x^{8} + 7872 x^{7} - 78834 x^{6} + 473634 x^{5} - 1747410 x^{4} + 3882224 x^{3} - 4846824 x^{2} + 2888640 x - 518400

Gráfica
02468-8-6-4-2-1010-500000000000500000000000
Primera derivada [src]
x*(x - 1)*(x - 2)*(x - 3)*(x - 4)*(x - 5)*(x - 6)*(x - 8)*(x - 9) + (x - 10)*(x*(x - 1)*(x - 2)*(x - 3)*(x - 4)*(x - 5)*(x - 6)*(x - 8) + (x - 9)*(x*(x - 1)*(x - 2)*(x - 3)*(x - 4)*(x - 5)*(x - 6) + (x - 8)*(x*(x - 1)*(x - 2)*(x - 3)*(x - 4)*(x - 5) + (x - 6)*(x*(x - 1)*(x - 2)*(x - 3)*(x - 4) + (x - 5)*(x*(x - 1)*(x - 2)*(x - 3) + (x - 4)*(x*(x - 1)*(x - 2) + (x - 3)*(x*(x - 1) + (-1 + 2*x)*(x - 2))))))))
x(x1)(x2)(x3)(x4)(x5)(x6)(x8)(x9)+(x10)(x(x1)(x2)(x3)(x4)(x5)(x6)(x8)+(x9)(x(x1)(x2)(x3)(x4)(x5)(x6)+(x8)(x(x1)(x2)(x3)(x4)(x5)+(x6)(x(x1)(x2)(x3)(x4)+(x5)(x(x1)(x2)(x3)+(x4)(x(x1)(x2)+(x3)(x(x1)+(x2)(2x1))))))))x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) \left(x - 5\right) \left(x - 6\right) \left(x - 8\right) \left(x - 9\right) + \left(x - 10\right) \left(x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) \left(x - 5\right) \left(x - 6\right) \left(x - 8\right) + \left(x - 9\right) \left(x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) \left(x - 5\right) \left(x - 6\right) + \left(x - 8\right) \left(x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) \left(x - 5\right) + \left(x - 6\right) \left(x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right) + \left(x - 5\right) \left(x \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) + \left(x - 4\right) \left(x \left(x - 1\right) \left(x - 2\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right)\right)\right)\right)\right)\right)
Segunda derivada [src]
2*((-10 + x)*((-9 + x)*((-8 + x)*((-6 + x)*((-5 + x)*((-4 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x) + 3*(-1 + x)*(-3 + x)) + (-3 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x)) + x*(-1 + x)*(-2 + x)) + (-4 + x)*((-3 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x)) + x*(-1 + x)*(-2 + x)) + x*(-1 + x)*(-3 + x)*(-2 + x)) + (-5 + x)*((-4 + x)*((-3 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x)) + x*(-1 + x)*(-2 + x)) + x*(-1 + x)*(-3 + x)*(-2 + x)) + x*(-1 + x)*(-4 + x)*(-3 + x)*(-2 + x)) + (-6 + x)*((-5 + x)*((-4 + x)*((-3 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x)) + x*(-1 + x)*(-2 + x)) + x*(-1 + x)*(-3 + x)*(-2 + x)) + x*(-1 + x)*(-4 + x)*(-3 + x)*(-2 + x)) + x*(-1 + x)*(-5 + x)*(-4 + x)*(-3 + x)*(-2 + x)) + (-8 + x)*((-6 + x)*((-5 + x)*((-4 + x)*((-3 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x)) + x*(-1 + x)*(-2 + x)) + x*(-1 + x)*(-3 + x)*(-2 + x)) + x*(-1 + x)*(-4 + x)*(-3 + x)*(-2 + x)) + x*(-1 + x)*(-5 + x)*(-4 + x)*(-3 + x)*(-2 + x)) + x*(-1 + x)*(-6 + x)*(-5 + x)*(-4 + x)*(-3 + x)*(-2 + x)) + (-9 + x)*((-8 + x)*((-6 + x)*((-5 + x)*((-4 + x)*((-3 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x)) + x*(-1 + x)*(-2 + x)) + x*(-1 + x)*(-3 + x)*(-2 + x)) + x*(-1 + x)*(-4 + x)*(-3 + x)*(-2 + x)) + x*(-1 + x)*(-5 + x)*(-4 + x)*(-3 + x)*(-2 + x)) + x*(-1 + x)*(-6 + x)*(-5 + x)*(-4 + x)*(-3 + x)*(-2 + x)) + x*(-1 + x)*(-8 + x)*(-6 + x)*(-5 + x)*(-4 + x)*(-3 + x)*(-2 + x))
2(x(x8)(x6)(x5)(x4)(x3)(x2)(x1)+(x10)(x(x6)(x5)(x4)(x3)(x2)(x1)+(x9)(x(x5)(x4)(x3)(x2)(x1)+(x8)(x(x4)(x3)(x2)(x1)+(x6)(x(x3)(x2)(x1)+(x5)(x(x2)(x1)+(x4)(x(x1)+3(x3)(x1)+(x2)(2x1))+(x3)(x(x1)+(x2)(2x1)))+(x4)(x(x2)(x1)+(x3)(x(x1)+(x2)(2x1))))+(x5)(x(x3)(x2)(x1)+(x4)(x(x2)(x1)+(x3)(x(x1)+(x2)(2x1)))))+(x6)(x(x4)(x3)(x2)(x1)+(x5)(x(x3)(x2)(x1)+(x4)(x(x2)(x1)+(x3)(x(x1)+(x2)(2x1))))))+(x8)(x(x5)(x4)(x3)(x2)(x1)+(x6)(x(x4)(x3)(x2)(x1)+(x5)(x(x3)(x2)(x1)+(x4)(x(x2)(x1)+(x3)(x(x1)+(x2)(2x1)))))))+(x9)(x(x6)(x5)(x4)(x3)(x2)(x1)+(x8)(x(x5)(x4)(x3)(x2)(x1)+(x6)(x(x4)(x3)(x2)(x1)+(x5)(x(x3)(x2)(x1)+(x4)(x(x2)(x1)+(x3)(x(x1)+(x2)(2x1))))))))2 \left(x \left(x - 8\right) \left(x - 6\right) \left(x - 5\right) \left(x - 4\right) \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 10\right) \left(x \left(x - 6\right) \left(x - 5\right) \left(x - 4\right) \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 9\right) \left(x \left(x - 5\right) \left(x - 4\right) \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 8\right) \left(x \left(x - 4\right) \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 6\right) \left(x \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 5\right) \left(x \left(x - 2\right) \left(x - 1\right) + \left(x - 4\right) \left(x \left(x - 1\right) + 3 \left(x - 3\right) \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right) + \left(x - 4\right) \left(x \left(x - 2\right) \left(x - 1\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right)\right) + \left(x - 5\right) \left(x \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 4\right) \left(x \left(x - 2\right) \left(x - 1\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right)\right)\right) + \left(x - 6\right) \left(x \left(x - 4\right) \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 5\right) \left(x \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 4\right) \left(x \left(x - 2\right) \left(x - 1\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right)\right)\right)\right) + \left(x - 8\right) \left(x \left(x - 5\right) \left(x - 4\right) \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 6\right) \left(x \left(x - 4\right) \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 5\right) \left(x \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 4\right) \left(x \left(x - 2\right) \left(x - 1\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right)\right)\right)\right)\right) + \left(x - 9\right) \left(x \left(x - 6\right) \left(x - 5\right) \left(x - 4\right) \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 8\right) \left(x \left(x - 5\right) \left(x - 4\right) \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 6\right) \left(x \left(x - 4\right) \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 5\right) \left(x \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 4\right) \left(x \left(x - 2\right) \left(x - 1\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right)\right)\right)\right)\right)\right)
Tercera derivada [src]
6*((-10 + x)*((-9 + x)*((-8 + x)*((-6 + x)*((-5 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x) + 2*(-4 + x)*(-3 + 2*x) + 3*(-1 + x)*(-3 + x)) + (-4 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x) + 3*(-1 + x)*(-3 + x)) + (-3 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x)) + x*(-1 + x)*(-2 + x)) + (-5 + x)*((-4 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x) + 3*(-1 + x)*(-3 + x)) + (-3 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x)) + x*(-1 + x)*(-2 + x)) + (-4 + x)*((-3 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x)) + x*(-1 + x)*(-2 + x)) + x*(-1 + x)*(-3 + x)*(-2 + x)) + (-6 + x)*((-5 + x)*((-4 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x) + 3*(-1 + x)*(-3 + x)) + (-3 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x)) + x*(-1 + x)*(-2 + x)) + (-4 + x)*((-3 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x)) + x*(-1 + x)*(-2 + x)) + x*(-1 + x)*(-3 + x)*(-2 + x)) + (-5 + x)*((-4 + x)*((-3 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x)) + x*(-1 + x)*(-2 + x)) + x*(-1 + x)*(-3 + x)*(-2 + x)) + x*(-1 + x)*(-4 + x)*(-3 + x)*(-2 + x)) + (-8 + x)*((-6 + x)*((-5 + x)*((-4 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x) + 3*(-1 + x)*(-3 + x)) + (-3 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x)) + x*(-1 + x)*(-2 + x)) + (-4 + x)*((-3 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x)) + x*(-1 + x)*(-2 + x)) + x*(-1 + x)*(-3 + x)*(-2 + x)) + (-5 + x)*((-4 + x)*((-3 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x)) + x*(-1 + x)*(-2 + x)) + x*(-1 + x)*(-3 + x)*(-2 + x)) + x*(-1 + x)*(-4 + x)*(-3 + x)*(-2 + x)) + (-6 + x)*((-5 + x)*((-4 + x)*((-3 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x)) + x*(-1 + x)*(-2 + x)) + x*(-1 + x)*(-3 + x)*(-2 + x)) + x*(-1 + x)*(-4 + x)*(-3 + x)*(-2 + x)) + x*(-1 + x)*(-5 + x)*(-4 + x)*(-3 + x)*(-2 + x)) + (-9 + x)*((-8 + x)*((-6 + x)*((-5 + x)*((-4 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x) + 3*(-1 + x)*(-3 + x)) + (-3 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x)) + x*(-1 + x)*(-2 + x)) + (-4 + x)*((-3 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x)) + x*(-1 + x)*(-2 + x)) + x*(-1 + x)*(-3 + x)*(-2 + x)) + (-5 + x)*((-4 + x)*((-3 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x)) + x*(-1 + x)*(-2 + x)) + x*(-1 + x)*(-3 + x)*(-2 + x)) + x*(-1 + x)*(-4 + x)*(-3 + x)*(-2 + x)) + (-6 + x)*((-5 + x)*((-4 + x)*((-3 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x)) + x*(-1 + x)*(-2 + x)) + x*(-1 + x)*(-3 + x)*(-2 + x)) + x*(-1 + x)*(-4 + x)*(-3 + x)*(-2 + x)) + x*(-1 + x)*(-5 + x)*(-4 + x)*(-3 + x)*(-2 + x)) + (-8 + x)*((-6 + x)*((-5 + x)*((-4 + x)*((-3 + x)*(x*(-1 + x) + (-1 + 2*x)*(-2 + x)) + x*(-1 + x)*(-2 + x)) + x*(-1 + x)*(-3 + x)*(-2 + x)) + x*(-1 + x)*(-4 + x)*(-3 + x)*(-2 + x)) + x*(-1 + x)*(-5 + x)*(-4 + x)*(-3 + x)*(-2 + x)) + x*(-1 + x)*(-6 + x)*(-5 + x)*(-4 + x)*(-3 + x)*(-2 + x))
6(x(x6)(x5)(x4)(x3)(x2)(x1)+(x10)(x(x5)(x4)(x3)(x2)(x1)+(x9)(x(x4)(x3)(x2)(x1)+(x8)(x(x3)(x2)(x1)+(x6)(x(x2)(x1)+(x5)(x(x1)+2(x4)(2x3)+3(x3)(x1)+(x2)(2x1))+(x4)(x(x1)+3(x3)(x1)+(x2)(2x1))+(x3)(x(x1)+(x2)(2x1)))+(x5)(x(x2)(x1)+(x4)(x(x1)+3(x3)(x1)+(x2)(2x1))+(x3)(x(x1)+(x2)(2x1)))+(x4)(x(x2)(x1)+(x3)(x(x1)+(x2)(2x1))))+(x6)(x(x3)(x2)(x1)+(x5)(x(x2)(x1)+(x4)(x(x1)+3(x3)(x1)+(x2)(2x1))+(x3)(x(x1)+(x2)(2x1)))+(x4)(x(x2)(x1)+(x3)(x(x1)+(x2)(2x1))))+(x5)(x(x3)(x2)(x1)+(x4)(x(x2)(x1)+(x3)(x(x1)+(x2)(2x1)))))+(x8)(x(x4)(x3)(x2)(x1)+(x6)(x(x3)(x2)(x1)+(x5)(x(x2)(x1)+(x4)(x(x1)+3(x3)(x1)+(x2)(2x1))+(x3)(x(x1)+(x2)(2x1)))+(x4)(x(x2)(x1)+(x3)(x(x1)+(x2)(2x1))))+(x5)(x(x3)(x2)(x1)+(x4)(x(x2)(x1)+(x3)(x(x1)+(x2)(2x1)))))+(x6)(x(x4)(x3)(x2)(x1)+(x5)(x(x3)(x2)(x1)+(x4)(x(x2)(x1)+(x3)(x(x1)+(x2)(2x1))))))+(x9)(x(x5)(x4)(x3)(x2)(x1)+(x8)(x(x4)(x3)(x2)(x1)+(x6)(x(x3)(x2)(x1)+(x5)(x(x2)(x1)+(x4)(x(x1)+3(x3)(x1)+(x2)(2x1))+(x3)(x(x1)+(x2)(2x1)))+(x4)(x(x2)(x1)+(x3)(x(x1)+(x2)(2x1))))+(x5)(x(x3)(x2)(x1)+(x4)(x(x2)(x1)+(x3)(x(x1)+(x2)(2x1)))))+(x6)(x(x4)(x3)(x2)(x1)+(x5)(x(x3)(x2)(x1)+(x4)(x(x2)(x1)+(x3)(x(x1)+(x2)(2x1))))))+(x8)(x(x5)(x4)(x3)(x2)(x1)+(x6)(x(x4)(x3)(x2)(x1)+(x5)(x(x3)(x2)(x1)+(x4)(x(x2)(x1)+(x3)(x(x1)+(x2)(2x1)))))))6 \left(x \left(x - 6\right) \left(x - 5\right) \left(x - 4\right) \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 10\right) \left(x \left(x - 5\right) \left(x - 4\right) \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 9\right) \left(x \left(x - 4\right) \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 8\right) \left(x \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 6\right) \left(x \left(x - 2\right) \left(x - 1\right) + \left(x - 5\right) \left(x \left(x - 1\right) + 2 \left(x - 4\right) \left(2 x - 3\right) + 3 \left(x - 3\right) \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right) + \left(x - 4\right) \left(x \left(x - 1\right) + 3 \left(x - 3\right) \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right) + \left(x - 5\right) \left(x \left(x - 2\right) \left(x - 1\right) + \left(x - 4\right) \left(x \left(x - 1\right) + 3 \left(x - 3\right) \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right) + \left(x - 4\right) \left(x \left(x - 2\right) \left(x - 1\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right)\right) + \left(x - 6\right) \left(x \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 5\right) \left(x \left(x - 2\right) \left(x - 1\right) + \left(x - 4\right) \left(x \left(x - 1\right) + 3 \left(x - 3\right) \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right) + \left(x - 4\right) \left(x \left(x - 2\right) \left(x - 1\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right)\right) + \left(x - 5\right) \left(x \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 4\right) \left(x \left(x - 2\right) \left(x - 1\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right)\right)\right) + \left(x - 8\right) \left(x \left(x - 4\right) \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 6\right) \left(x \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 5\right) \left(x \left(x - 2\right) \left(x - 1\right) + \left(x - 4\right) \left(x \left(x - 1\right) + 3 \left(x - 3\right) \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right) + \left(x - 4\right) \left(x \left(x - 2\right) \left(x - 1\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right)\right) + \left(x - 5\right) \left(x \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 4\right) \left(x \left(x - 2\right) \left(x - 1\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right)\right)\right) + \left(x - 6\right) \left(x \left(x - 4\right) \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 5\right) \left(x \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 4\right) \left(x \left(x - 2\right) \left(x - 1\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right)\right)\right)\right) + \left(x - 9\right) \left(x \left(x - 5\right) \left(x - 4\right) \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 8\right) \left(x \left(x - 4\right) \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 6\right) \left(x \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 5\right) \left(x \left(x - 2\right) \left(x - 1\right) + \left(x - 4\right) \left(x \left(x - 1\right) + 3 \left(x - 3\right) \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right) + \left(x - 4\right) \left(x \left(x - 2\right) \left(x - 1\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right)\right) + \left(x - 5\right) \left(x \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 4\right) \left(x \left(x - 2\right) \left(x - 1\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right)\right)\right) + \left(x - 6\right) \left(x \left(x - 4\right) \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 5\right) \left(x \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 4\right) \left(x \left(x - 2\right) \left(x - 1\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right)\right)\right)\right) + \left(x - 8\right) \left(x \left(x - 5\right) \left(x - 4\right) \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 6\right) \left(x \left(x - 4\right) \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 5\right) \left(x \left(x - 3\right) \left(x - 2\right) \left(x - 1\right) + \left(x - 4\right) \left(x \left(x - 2\right) \left(x - 1\right) + \left(x - 3\right) \left(x \left(x - 1\right) + \left(x - 2\right) \left(2 x - 1\right)\right)\right)\right)\right)\right)\right)
Gráfico
Derivada de x*(x-1)*(x-2)*(x-3)*(x-4)*(x-5)*(x-6)*(x-8)*(x-9)*(x-10)