Sr Examen

Otras calculadoras


x((x*cos(x))^(x*cos(x))-(x^2)*cos(x)*sin(x))
  • ¿Cómo usar?

  • Derivada de:
  • Derivada de 7^(3*x-1) Derivada de 7^(3*x-1)
  • Derivada de 6^(x^2-8x+28) Derivada de 6^(x^2-8x+28)
  • Derivada de -5*tan(2*t)-4*cot(4*t) Derivada de -5*tan(2*t)-4*cot(4*t)
  • Derivada de 5(3-2x)^2 Derivada de 5(3-2x)^2
  • Expresiones idénticas

  • x((x*cos(x))^(x*cos(x))-(x^ dos)*cos(x)*sin(x))
  • x((x multiplicar por coseno de (x)) en el grado (x multiplicar por coseno de (x)) menos (x al cuadrado ) multiplicar por coseno de (x) multiplicar por seno de (x))
  • x((x multiplicar por coseno de (x)) en el grado (x multiplicar por coseno de (x)) menos (x en el grado dos) multiplicar por coseno de (x) multiplicar por seno de (x))
  • x((x*cos(x))(x*cos(x))-(x2)*cos(x)*sin(x))
  • xx*cosxx*cosx-x2*cosx*sinx
  • x((x*cos(x))^(x*cos(x))-(x²)*cos(x)*sin(x))
  • x((x*cos(x)) en el grado (x*cos(x))-(x en el grado 2)*cos(x)*sin(x))
  • x((xcos(x))^(xcos(x))-(x^2)cos(x)sin(x))
  • x((xcos(x))(xcos(x))-(x2)cos(x)sin(x))
  • xxcosxxcosx-x2cosxsinx
  • xxcosx^xcosx-x^2cosxsinx
  • Expresiones semejantes

  • x((x*cos(x))^(x*cos(x))+(x^2)*cos(x)*sin(x))
  • x((x*cosx)^(x*cosx)-(x^2)*cosx*sinx)

Derivada de x((x*cos(x))^(x*cos(x))-(x^2)*cos(x)*sin(x))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
  /          x*cos(x)    2              \
x*\(x*cos(x))         - x *cos(x)*sin(x)/
x((xcos(x))xcos(x)x2cos(x)sin(x))x \left(\left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}} - x^{2} \cos{\left(x \right)} \sin{\left(x \right)}\right)
x*((x*cos(x))^(x*cos(x)) - x^2*cos(x)*sin(x))
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)=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)=(xcos(x))xcos(x)x2cos(x)sin(x)g{\left(x \right)} = \left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}} - x^{2} \cos{\left(x \right)} \sin{\left(x \right)}; calculamos ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. diferenciamos (xcos(x))xcos(x)x2cos(x)sin(x)\left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}} - x^{2} \cos{\left(x \right)} \sin{\left(x \right)} miembro por miembro:

      1. No logro encontrar los pasos en la búsqueda de esta derivada.

        Perola derivada

        (xcos(x))xcos(x)(log(xcos(x))+1)\left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}} \left(\log{\left(x \cos{\left(x \right)} \right)} + 1\right)

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

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

          ddxf(x)g(x)h(x)=f(x)g(x)ddxh(x)+f(x)h(x)ddxg(x)+g(x)h(x)ddxf(x)\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} h{\left(x \right)} = f{\left(x \right)} g{\left(x \right)} \frac{d}{d x} h{\left(x \right)} + f{\left(x \right)} h{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} h{\left(x \right)} \frac{d}{d x} f{\left(x \right)}

          f(x)=x2f{\left(x \right)} = x^{2}; calculamos ddxf(x)\frac{d}{d x} f{\left(x \right)}:

          1. Según el principio, aplicamos: x2x^{2} tenemos 2x2 x

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

          1. La derivada del coseno es igual a menos el seno:

            ddxcos(x)=sin(x)\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}

          h(x)=sin(x)h{\left(x \right)} = \sin{\left(x \right)}; calculamos ddxh(x)\frac{d}{d x} h{\left(x \right)}:

          1. La derivada del seno es igual al coseno:

            ddxsin(x)=cos(x)\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}

          Como resultado de: x2sin2(x)+x2cos2(x)+2xsin(x)cos(x)- x^{2} \sin^{2}{\left(x \right)} + x^{2} \cos^{2}{\left(x \right)} + 2 x \sin{\left(x \right)} \cos{\left(x \right)}

        Entonces, como resultado: x2sin2(x)x2cos2(x)2xsin(x)cos(x)x^{2} \sin^{2}{\left(x \right)} - x^{2} \cos^{2}{\left(x \right)} - 2 x \sin{\left(x \right)} \cos{\left(x \right)}

      Como resultado de: x2sin2(x)x2cos2(x)2xsin(x)cos(x)+(xcos(x))xcos(x)(log(xcos(x))+1)x^{2} \sin^{2}{\left(x \right)} - x^{2} \cos^{2}{\left(x \right)} - 2 x \sin{\left(x \right)} \cos{\left(x \right)} + \left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}} \left(\log{\left(x \cos{\left(x \right)} \right)} + 1\right)

    Como resultado de: x(x2sin2(x)x2cos2(x)2xsin(x)cos(x)+(xcos(x))xcos(x)(log(xcos(x))+1))+(xcos(x))xcos(x)x2cos(x)sin(x)x \left(x^{2} \sin^{2}{\left(x \right)} - x^{2} \cos^{2}{\left(x \right)} - 2 x \sin{\left(x \right)} \cos{\left(x \right)} + \left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}} \left(\log{\left(x \cos{\left(x \right)} \right)} + 1\right)\right) + \left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}} - x^{2} \cos{\left(x \right)} \sin{\left(x \right)}

  2. Simplificamos:

    x3cos(2x)3x2sin(2x)2+x(xcos(x))xcos(x)log(xcos(x))+x(xcos(x))xcos(x)+(xcos(x))xcos(x)- x^{3} \cos{\left(2 x \right)} - \frac{3 x^{2} \sin{\left(2 x \right)}}{2} + x \left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}} \log{\left(x \cos{\left(x \right)} \right)} + x \left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}} + \left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}}


Respuesta:

x3cos(2x)3x2sin(2x)2+x(xcos(x))xcos(x)log(xcos(x))+x(xcos(x))xcos(x)+(xcos(x))xcos(x)- x^{3} \cos{\left(2 x \right)} - \frac{3 x^{2} \sin{\left(2 x \right)}}{2} + x \left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}} \log{\left(x \cos{\left(x \right)} \right)} + x \left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}} + \left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}}

Gráfica
02468-8-6-4-2-1010-100000000000100000000000
Primera derivada [src]
          x*cos(x)     /          x*cos(x)                                                            / 2                    \           2    2   \    2              
(x*cos(x))         + x*\(x*cos(x))        *((-x*sin(x) + cos(x))*log(x*cos(x)) - x*sin(x) + cos(x)) + \x *sin(x) - 2*x*cos(x)/*sin(x) - x *cos (x)/ - x *cos(x)*sin(x)
x(x2cos2(x)+(xcos(x))xcos(x)(xsin(x)+(xsin(x)+cos(x))log(xcos(x))+cos(x))+(x2sin(x)2xcos(x))sin(x))+(xcos(x))xcos(x)x2cos(x)sin(x)x \left(- x^{2} \cos^{2}{\left(x \right)} + \left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}} \left(- x \sin{\left(x \right)} + \left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right) \log{\left(x \cos{\left(x \right)} \right)} + \cos{\left(x \right)}\right) + \left(x^{2} \sin{\left(x \right)} - 2 x \cos{\left(x \right)}\right) \sin{\left(x \right)}\right) + \left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}} - x^{2} \cos{\left(x \right)} \sin{\left(x \right)}
Segunda derivada [src]
  /                                                                                                                                                 /                                                                                2\                                                                     \                                                                                                                                    
  |          x*cos(x)                                                          2   /             2                    \                    x*cos(x) |                                                            (-cos(x) + x*sin(x)) |          2                                           2              |      2    2                  x*cos(x)                                                                                              
x*|(x*cos(x))        *(-cos(x) + x*sin(x) + (-cos(x) + x*sin(x))*log(x*cos(x)))  + \-2*cos(x) + x *cos(x) + 4*x*sin(x)/*sin(x) - (x*cos(x))        *|2*sin(x) + x*cos(x) + (2*sin(x) + x*cos(x))*log(x*cos(x)) - ---------------------| - 2*x*cos (x) + x*(-2*cos(x) + x*sin(x))*cos(x) + 2*x *cos(x)*sin(x)| - 2*x *cos (x) - 2*(x*cos(x))        *(-cos(x) + x*sin(x) + (-cos(x) + x*sin(x))*log(x*cos(x))) + 2*x*(-2*cos(x) + x*sin(x))*sin(x)
  \                                                                                                                                                 \                                                                   x*cos(x)      /                                                                     /                                                                                                                                    
2x2cos2(x)+2x(xsin(x)2cos(x))sin(x)+x(2x2sin(x)cos(x)+x(xsin(x)2cos(x))cos(x)2xcos2(x)+(xcos(x))xcos(x)(xsin(x)+(xsin(x)cos(x))log(xcos(x))cos(x))2(xcos(x))xcos(x)(xcos(x)+(xcos(x)+2sin(x))log(xcos(x))+2sin(x)(xsin(x)cos(x))2xcos(x))+(x2cos(x)+4xsin(x)2cos(x))sin(x))2(xcos(x))xcos(x)(xsin(x)+(xsin(x)cos(x))log(xcos(x))cos(x))- 2 x^{2} \cos^{2}{\left(x \right)} + 2 x \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \sin{\left(x \right)} + x \left(2 x^{2} \sin{\left(x \right)} \cos{\left(x \right)} + x \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \cos{\left(x \right)} - 2 x \cos^{2}{\left(x \right)} + \left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}} \left(x \sin{\left(x \right)} + \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \cos{\left(x \right)} \right)} - \cos{\left(x \right)}\right)^{2} - \left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}} \left(x \cos{\left(x \right)} + \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \log{\left(x \cos{\left(x \right)} \right)} + 2 \sin{\left(x \right)} - \frac{\left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}{x \cos{\left(x \right)}}\right) + \left(x^{2} \cos{\left(x \right)} + 4 x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \sin{\left(x \right)}\right) - 2 \left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}} \left(x \sin{\left(x \right)} + \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \cos{\left(x \right)} \right)} - \cos{\left(x \right)}\right)
Tercera derivada [src]
  /                                 /                                                                                  2                       2                                                      \                                                                                                                                                                                                                                                                                                                               /                                                                                2\                    \                                      /                                                                                2\                                                                                                                                                                                           
  |       2                x*cos(x) |                                                              (-cos(x) + x*sin(x))    (-cos(x) + x*sin(x)) *sin(x)   3*(-cos(x) + x*sin(x))*(2*sin(x) + x*cos(x))|   /            2                    \                    x*cos(x)                                                          3      2    2         2    2        /             2                    \                                                        x*cos(x)                                                           |                                                            (-cos(x) + x*sin(x)) |                    |          2                  x*cos(x) |                                                            (-cos(x) + x*sin(x)) |               x*cos(x)                                                          2     /             2                    \                                                 2              
x*|- 2*cos (x) + (x*cos(x))        *|-3*cos(x) + x*sin(x) + (-3*cos(x) + x*sin(x))*log(x*cos(x)) - --------------------- + ---------------------------- + --------------------------------------------| + \6*sin(x) - x *sin(x) + 6*x*cos(x)/*sin(x) - (x*cos(x))        *(-cos(x) + x*sin(x) + (-cos(x) + x*sin(x))*log(x*cos(x)))  - 2*x *sin (x) + 2*x *cos (x) + 2*\-2*cos(x) + x *cos(x) + 4*x*sin(x)/*cos(x) - x*(-2*cos(x) + x*sin(x))*sin(x) + 3*(x*cos(x))        *(-cos(x) + x*sin(x) + (-cos(x) + x*sin(x))*log(x*cos(x)))*|2*sin(x) + x*cos(x) + (2*sin(x) + x*cos(x))*log(x*cos(x)) - ---------------------| + 8*x*cos(x)*sin(x)| - 6*x*cos (x) - 3*(x*cos(x))        *|2*sin(x) + x*cos(x) + (2*sin(x) + x*cos(x))*log(x*cos(x)) - ---------------------| + 3*(x*cos(x))        *(-cos(x) + x*sin(x) + (-cos(x) + x*sin(x))*log(x*cos(x)))  + 3*\-2*cos(x) + x *cos(x) + 4*x*sin(x)/*sin(x) + 3*x*(-2*cos(x) + x*sin(x))*cos(x) + 6*x *cos(x)*sin(x)
  |                                 |                                                                     2                              2                                  x*cos(x)                  |                                                                                                                                                                                                                                                                                                                               \                                                                   x*cos(x)      /                    |                                      \                                                                   x*cos(x)      /                                                                                                                                                                                           
  \                                 \                                                                    x *cos(x)                  x*cos (x)                                                         /                                                                                                                                                                                                                                                                                                                                                                                                                                      /                                                                                                                                                                                                                                                                                                                    
6x2sin(x)cos(x)+3x(xsin(x)2cos(x))cos(x)+x(2x2sin2(x)+2x2cos2(x)x(xsin(x)2cos(x))sin(x)+8xsin(x)cos(x)(xcos(x))xcos(x)(xsin(x)+(xsin(x)cos(x))log(xcos(x))cos(x))3+3(xcos(x))xcos(x)(xsin(x)+(xsin(x)cos(x))log(xcos(x))cos(x))(xcos(x)+(xcos(x)+2sin(x))log(xcos(x))+2sin(x)(xsin(x)cos(x))2xcos(x))+(xcos(x))xcos(x)(xsin(x)+(xsin(x)3cos(x))log(xcos(x))3cos(x)+(xsin(x)cos(x))2sin(x)xcos2(x)+3(xsin(x)cos(x))(xcos(x)+2sin(x))xcos(x)(xsin(x)cos(x))2x2cos(x))+(x2sin(x)+6xcos(x)+6sin(x))sin(x)+2(x2cos(x)+4xsin(x)2cos(x))cos(x)2cos2(x))6xcos2(x)+3(xcos(x))xcos(x)(xsin(x)+(xsin(x)cos(x))log(xcos(x))cos(x))23(xcos(x))xcos(x)(xcos(x)+(xcos(x)+2sin(x))log(xcos(x))+2sin(x)(xsin(x)cos(x))2xcos(x))+3(x2cos(x)+4xsin(x)2cos(x))sin(x)6 x^{2} \sin{\left(x \right)} \cos{\left(x \right)} + 3 x \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \cos{\left(x \right)} + x \left(- 2 x^{2} \sin^{2}{\left(x \right)} + 2 x^{2} \cos^{2}{\left(x \right)} - x \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \sin{\left(x \right)} + 8 x \sin{\left(x \right)} \cos{\left(x \right)} - \left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}} \left(x \sin{\left(x \right)} + \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \cos{\left(x \right)} \right)} - \cos{\left(x \right)}\right)^{3} + 3 \left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}} \left(x \sin{\left(x \right)} + \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \cos{\left(x \right)} \right)} - \cos{\left(x \right)}\right) \left(x \cos{\left(x \right)} + \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \log{\left(x \cos{\left(x \right)} \right)} + 2 \sin{\left(x \right)} - \frac{\left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}{x \cos{\left(x \right)}}\right) + \left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}} \left(x \sin{\left(x \right)} + \left(x \sin{\left(x \right)} - 3 \cos{\left(x \right)}\right) \log{\left(x \cos{\left(x \right)} \right)} - 3 \cos{\left(x \right)} + \frac{\left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2} \sin{\left(x \right)}}{x \cos^{2}{\left(x \right)}} + \frac{3 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right)}{x \cos{\left(x \right)}} - \frac{\left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}{x^{2} \cos{\left(x \right)}}\right) + \left(- x^{2} \sin{\left(x \right)} + 6 x \cos{\left(x \right)} + 6 \sin{\left(x \right)}\right) \sin{\left(x \right)} + 2 \left(x^{2} \cos{\left(x \right)} + 4 x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \cos{\left(x \right)} - 2 \cos^{2}{\left(x \right)}\right) - 6 x \cos^{2}{\left(x \right)} + 3 \left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}} \left(x \sin{\left(x \right)} + \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \cos{\left(x \right)} \right)} - \cos{\left(x \right)}\right)^{2} - 3 \left(x \cos{\left(x \right)}\right)^{x \cos{\left(x \right)}} \left(x \cos{\left(x \right)} + \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \log{\left(x \cos{\left(x \right)} \right)} + 2 \sin{\left(x \right)} - \frac{\left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}{x \cos{\left(x \right)}}\right) + 3 \left(x^{2} \cos{\left(x \right)} + 4 x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \sin{\left(x \right)}
Gráfico
Derivada de x((x*cos(x))^(x*cos(x))-(x^2)*cos(x)*sin(x))