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y=sqrt(xcosxsqrt(1-e^x))
Derivada de la función/ 1-e^x/ xcosx/ xsqrt/ y=sqrt(xcosxsqrt(1-e^x))

Derivada de y=sqrt(xcosxsqrt(1-e^x))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    ______________________
   /             ________ 
  /             /      x  
\/   x*cos(x)*\/  1 - E
xcos⁡(x)1−ex\sqrt{x \cos{\left(x \right)} \sqrt{1 - e^{x}}} 
sqrt((x*cos(x))*sqrt(1 - E^x))
Solución detallada

  1. Sustituimos u=xcos⁡(x)1−exu = x \cos{\left(x \right)} \sqrt{1 - e^{x}}.

  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 ddxxcos⁡(x)1−ex\frac{d}{d x} x \cos{\left(x \right)} \sqrt{1 - e^{x}}:

    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)=xcos⁡(x)f{\left(x \right)} = x \cos{\left(x \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)=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)}

        Como resultado de: −xsin⁡(x)+cos⁡(x)- x \sin{\left(x \right)} + \cos{\left(x \right)}

      g(x)=1−exg{\left(x \right)} = \sqrt{1 - e^{x}}; calculamos ddxg(x)\frac{d}{d x} g{\left(x \right)}:

      1. Sustituimos u=1−exu = 1 - e^{x}.

      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(1−ex)\frac{d}{d x} \left(1 - e^{x}\right):

        1. diferenciamos 1−ex1 - e^{x} miembro por miembro:

          1. La derivada de una constante 11 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. Derivado exe^{x} es.

            Entonces, como resultado: −ex- e^{x}

          Como resultado de: −ex- e^{x}

        Como resultado de la secuencia de reglas:

        −ex21−ex- \frac{e^{x}}{2 \sqrt{1 - e^{x}}}

      Como resultado de: −xexcos⁡(x)21−ex+1−ex(−xsin⁡(x)+cos⁡(x))- \frac{x e^{x} \cos{\left(x \right)}}{2 \sqrt{1 - e^{x}}} + \sqrt{1 - e^{x}} \left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right)

    Como resultado de la secuencia de reglas:

    −xexcos⁡(x)21−ex+1−ex(−xsin⁡(x)+cos⁡(x))2x1−excos⁡(x)\frac{- \frac{x e^{x} \cos{\left(x \right)}}{2 \sqrt{1 - e^{x}}} + \sqrt{1 - e^{x}} \left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right)}{2 \sqrt{x \sqrt{1 - e^{x}} \cos{\left(x \right)}}}

  4. Simplificamos:

    −xexcos⁡(x)−2(xsin⁡(x)−cos⁡(x))(ex−1)4x1−excos⁡(x)1−ex- \frac{x e^{x} \cos{\left(x \right)} - 2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(e^{x} - 1\right)}{4 \sqrt{x \sqrt{1 - e^{x}} \cos{\left(x \right)}} \sqrt{1 - e^{x}}}

Respuesta:

−xexcos⁡(x)−2(xsin⁡(x)−cos⁡(x))(ex−1)4x1−excos⁡(x)1−ex- \frac{x e^{x} \cos{\left(x \right)} - 2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(e^{x} - 1\right)}{4 \sqrt{x \sqrt{1 - e^{x}} \cos{\left(x \right)}} \sqrt{1 - e^{x}}}

Gráfica
02468-8-6-4-2-1010-1010
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
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   /      ________         |  /      x                                    x |
  /      /      x          |\/  1 - E  *(-x*sin(x) + cos(x))    x*cos(x)*e  |
\/   x*\/  1 - E  *cos(x) *|-------------------------------- - -------------|
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                           |                                       /      x |
                           \                                   4*\/  1 - E  /
-----------------------------------------------------------------------------
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                                 /      x                                    
                             x*\/  1 - E  *cos(x)
x1−excos⁡(x)(−xexcos⁡(x)41−ex+1−ex(−xsin⁡(x)+cos⁡(x))2)x1−excos⁡(x)\frac{\sqrt{x \sqrt{1 - e^{x}} \cos{\left(x \right)}} \left(- \frac{x e^{x} \cos{\left(x \right)}}{4 \sqrt{1 - e^{x}}} + \frac{\sqrt{1 - e^{x}} \left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right)}{2}\right)}{x \sqrt{1 - e^{x}} \cos{\left(x \right)}}
Simplificar
Segunda derivada [src] 
                           /    /     ________                                                 x             x             2*x        x                      x\     /     ________                                  x\        /     ________                                  x\     /     ________                                  x\          /     ________                                  x\ /       ________                 ________                    x\\
                           |    |    /      x                          2*(-cos(x) + x*sin(x))*e    2*cos(x)*e    x*cos(x)*e      2*x*e *sin(x)   2*x*cos(x)*e |     |    /      x                         x*cos(x)*e |  x     |    /      x                         x*cos(x)*e |     |    /      x                         x*cos(x)*e |          |    /      x                         x*cos(x)*e | |      /      x                 /      x           x*cos(x)*e ||
                           |  2*|4*\/  1 - e  *(2*sin(x) + x*cos(x)) - ------------------------- + ----------- + ------------- - ------------- + -------------|   2*|2*\/  1 - e  *(-cos(x) + x*sin(x)) + -----------|*e    4*|2*\/  1 - e  *(-cos(x) + x*sin(x)) + -----------|   4*|2*\/  1 - e  *(-cos(x) + x*sin(x)) + -----------|*sin(x)   |2*\/  1 - e  *(-cos(x) + x*sin(x)) + -----------|*|- 2*\/  1 - e  *cos(x) + 2*x*\/  1 - e  *sin(x) + -----------||
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\/   x*\/  1 - e  *cos(x) *|- --------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------- + ---------------------------------------------------- - ----------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------|
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                           |                                                               /      x                                                                                     /     x\                                                   /      x                                               /      x                                                                               x*\-1 + e /*cos(x)                                                |
                           \                                                             \/  1 - e                                                                                      \1 - e /                                               x*\/  1 - e                                              \/  1 - e  *cos(x)                                                                                                                                         /
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                                                                                                                                                                                                                            16*x*cos(x)
x1−excos⁡(x)(−4(xexcos⁡(x)1−ex+21−ex(xsin⁡(x)−cos⁡(x)))sin⁡(x)1−excos⁡(x)−2(−2xexsin⁡(x)1−ex+2xexcos⁡(x)1−ex+xe2xcos⁡(x)(1−ex)32+41−ex(xcos⁡(x)+2sin⁡(x))−2(xsin⁡(x)−cos⁡(x))ex1−ex+2excos⁡(x)1−ex)1−ex−2(xexcos⁡(x)1−ex+21−ex(xsin⁡(x)−cos⁡(x)))ex(1−ex)32−(xexcos⁡(x)1−ex+21−ex(xsin⁡(x)−cos⁡(x)))(2x1−exsin⁡(x)+xexcos⁡(x)1−ex−21−excos⁡(x))x(ex−1)cos⁡(x)+4(xexcos⁡(x)1−ex+21−ex(xsin⁡(x)−cos⁡(x)))x1−ex)16xcos⁡(x)\frac{\sqrt{x \sqrt{1 - e^{x}} \cos{\left(x \right)}} \left(- \frac{4 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) \sin{\left(x \right)}}{\sqrt{1 - e^{x}} \cos{\left(x \right)}} - \frac{2 \left(- \frac{2 x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{2 x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{x e^{2 x} \cos{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + 4 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) - \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{2 e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}}\right)}{\sqrt{1 - e^{x}}} - \frac{2 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) e^{x}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} - \frac{\left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) \left(2 x \sqrt{1 - e^{x}} \sin{\left(x \right)} + \frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \cos{\left(x \right)}\right)}{x \left(e^{x} - 1\right) \cos{\left(x \right)}} + \frac{4 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right)}{x \sqrt{1 - e^{x}}}\right)}{16 x \cos{\left(x \right)}}
Simplificar
Tercera derivada [src] 
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                           |     /     ________                                  x\     /     ________                                    x             2*x                           2*x                           x                            x      x                      2*x               3*x        2*x               x       \      /     ________                                  x\      /     ________                                  x\          /     ________                                  x\        /     ________                                                 x             x             2*x        x                      x\         /     ________                                                 x             x             2*x        x                      x\              /     ________                                  x\      /     ________                                                 x             x             2*x        x                      x\             /     ________                                  x\      /       ________                 ________                    x\  /     ________                                  x\      /     ________                                  x\               /       ________                 ________                    x\ /     ________                                                 x             x             2*x        x                      x\     /     ________                                  x\ /     ________                 ________                    x             2*x        x                      x\      /     ________                                  x\ /       ________                 ________                    x\      /     ________                                  x\             /     ________                                  x\ /       ________                 ________                    x\            /     ________                                  x\ /       ________                 ________                    x\   |
                           |     |    /      x                         x*cos(x)*e |     |    /      x                           8*cos(x)*e    4*cos(x)*e      2*(-cos(x) + x*sin(x))*e      4*(-cos(x) + x*sin(x))*e    8*(2*sin(x) + x*cos(x))*e    8*e *sin(x)   6*x*cos(x)*e      3*x*cos(x)*e      4*x*e   *sin(x)   8*x*e *sin(x)|      |    /      x                         x*cos(x)*e |      |    /      x                         x*cos(x)*e |  2*x     |    /      x                         x*cos(x)*e |  x     |    /      x                          2*(-cos(x) + x*sin(x))*e    2*cos(x)*e    x*cos(x)*e      2*x*e *sin(x)   2*x*cos(x)*e |  x      |    /      x                          2*(-cos(x) + x*sin(x))*e    2*cos(x)*e    x*cos(x)*e      2*x*e *sin(x)   2*x*cos(x)*e |         2    |    /      x                         x*cos(x)*e |      |    /      x                          2*(-cos(x) + x*sin(x))*e    2*cos(x)*e    x*cos(x)*e      2*x*e *sin(x)   2*x*cos(x)*e |             |    /      x                         x*cos(x)*e |  x   |      /      x                 /      x           x*cos(x)*e |  |    /      x                         x*cos(x)*e |      |    /      x                         x*cos(x)*e |  x            |      /      x                 /      x           x*cos(x)*e | |    /      x                          2*(-cos(x) + x*sin(x))*e    2*cos(x)*e    x*cos(x)*e      2*x*e *sin(x)   2*x*cos(x)*e |     |    /      x                         x*cos(x)*e | |    /      x                 /      x           4*cos(x)*e    x*cos(x)*e      4*x*e *sin(x)   2*x*cos(x)*e |      |    /      x                         x*cos(x)*e | |      /      x                 /      x           x*cos(x)*e |      |    /      x                         x*cos(x)*e |             |    /      x                         x*cos(x)*e | |      /      x                 /      x           x*cos(x)*e |            |    /      x                         x*cos(x)*e | |      /      x                 /      x           x*cos(x)*e |  x|
                           |  16*|2*\/  1 - e  *(-cos(x) + x*sin(x)) + -----------|   4*|8*\/  1 - e  *(-3*cos(x) + x*sin(x)) - ----------- - ------------- + --------------------------- + ------------------------- + -------------------------- + ----------- - --------------- - --------------- + --------------- + -------------|   32*|2*\/  1 - e  *(-cos(x) + x*sin(x)) + -----------|   12*|2*\/  1 - e  *(-cos(x) + x*sin(x)) + -----------|*e      8*|2*\/  1 - e  *(-cos(x) + x*sin(x)) + -----------|*e    8*|4*\/  1 - e  *(2*sin(x) + x*cos(x)) - ------------------------- + ----------- + ------------- - ------------- + -------------|*e    16*|4*\/  1 - e  *(2*sin(x) + x*cos(x)) - ------------------------- + ----------- + ------------- - ------------- + -------------|   32*sin (x)*|2*\/  1 - e  *(-cos(x) + x*sin(x)) + -----------|   16*|4*\/  1 - e  *(2*sin(x) + x*cos(x)) - ------------------------- + ----------- + ------------- - ------------- + -------------|*sin(x)   16*|2*\/  1 - e  *(-cos(x) + x*sin(x)) + -----------|*e    |- 2*\/  1 - e  *cos(x) + 2*x*\/  1 - e  *sin(x) + -----------| *|2*\/  1 - e  *(-cos(x) + x*sin(x)) + -----------|   16*|2*\/  1 - e  *(-cos(x) + x*sin(x)) + -----------|*e *sin(x)   4*|- 2*\/  1 - e  *cos(x) + 2*x*\/  1 - e  *sin(x) + -----------|*|4*\/  1 - e  *(2*sin(x) + x*cos(x)) - ------------------------- + ----------- + ------------- - ------------- + -------------|   2*|2*\/  1 - e  *(-cos(x) + x*sin(x)) + -----------|*|8*\/  1 - e  *sin(x) + 4*x*\/  1 - e  *cos(x) + ----------- + ------------- - ------------- + -------------|   12*|2*\/  1 - e  *(-cos(x) + x*sin(x)) + -----------|*|- 2*\/  1 - e  *cos(x) + 2*x*\/  1 - e  *sin(x) + -----------|   32*|2*\/  1 - e  *(-cos(x) + x*sin(x)) + -----------|*sin(x)   12*|2*\/  1 - e  *(-cos(x) + x*sin(x)) + -----------|*|- 2*\/  1 - e  *cos(x) + 2*x*\/  1 - e  *sin(x) + -----------|*sin(x)   6*|2*\/  1 - e  *(-cos(x) + x*sin(x)) + -----------|*|- 2*\/  1 - e  *cos(x) + 2*x*\/  1 - e  *sin(x) + -----------|*e |
    ______________________ |     |                                        ________|     |                                          ________            3/2                    3/2                     ________                    ________              ________             3/2               5/2               3/2         ________ |      |                                        ________|      |                                        ________|          |                                        ________|        |                                                ________             ________            3/2        ________        ________ |         |                                                ________             ________            3/2        ________        ________ |              |                                        ________|      |                                                ________             ________            3/2        ________        ________ |             |                                        ________|      |                                                     ________|  |                                        ________|      |                                        ________|               |                                                     ________| |                                                ________             ________            3/2        ________        ________ |     |                                        ________| |                                                   ________            3/2        ________        ________ |      |                                        ________| |                                                     ________|      |                                        ________|             |                                        ________| |                                                     ________|            |                                        ________| |                                                     ________|   |
   /      ________         |     |                                       /      x |     |                                         /      x     /     x\               /     x\                       /      x                    /      x              /      x      /     x\          /     x\          /     x\           /      x  |      |                                       /      x |      |                                       /      x |          |                                       /      x |        |                                               /      x             /      x     /     x\          /      x        /      x  |         |                                               /      x             /      x     /     x\          /      x        /      x  |              |                                       /      x |      |                                               /      x             /      x     /     x\          /      x        /      x  |             |                                       /      x |      |                                                    /      x |  |                                       /      x |      |                                       /      x |               |                                                    /      x | |                                               /      x             /      x     /     x\          /      x        /      x  |     |                                       /      x | |                                                  /      x     /     x\          /      x        /      x  |      |                                       /      x | |                                                    /      x |      |                                       /      x |             |                                       /      x | |                                                    /      x |            |                                       /      x | |                                                    /      x |   |
  /      /      x          |     \                                     \/  1 - e  /     \                                       \/  1 - e      \1 - e /               \1 - e /                     \/  1 - e                   \/  1 - e             \/  1 - e       \1 - e /          \1 - e /          \1 - e /         \/  1 - e   /      \                                     \/  1 - e  /      \                                     \/  1 - e  /          \                                     \/  1 - e  /        \                                             \/  1 - e            \/  1 - e      \1 - e /        \/  1 - e       \/  1 - e   /         \                                             \/  1 - e            \/  1 - e      \1 - e /        \/  1 - e       \/  1 - e   /              \                                     \/  1 - e  /      \                                             \/  1 - e            \/  1 - e      \1 - e /        \/  1 - e       \/  1 - e   /             \                                     \/  1 - e  /      \                                                  \/  1 - e  /  \                                     \/  1 - e  /      \                                     \/  1 - e  /               \                                                  \/  1 - e  / \                                             \/  1 - e            \/  1 - e      \1 - e /        \/  1 - e       \/  1 - e   /     \                                     \/  1 - e  / \                                                \/  1 - e      \1 - e /        \/  1 - e       \/  1 - e   /      \                                     \/  1 - e  / \                                                  \/  1 - e  /      \                                     \/  1 - e  /             \                                     \/  1 - e  / \                                                  \/  1 - e  /            \                                     \/  1 - e  / \                                                  \/  1 - e  /   |
\/   x*\/  1 - e  *cos(x) *|- ----------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------- - ---------------------------------------------------------- - ------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------ - ---------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------|
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                           \                       \/  1 - e                                                                                                                                             \/  1 - e                                                                                                                                            x *\/  1 - e                                               \1 - e /                                                    \1 - e /                                                                                        \1 - e /                                                                                                                             x*\/  1 - e                                                                                     \/  1 - e  *cos (x)                                                                                    \/  1 - e  *cos(x)                                                                                   x*\1 - e /                                                                           x *\1 - e /   *cos (x)                                                                        \1 - e /   *cos(x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              x*\/  1 - e  *cos(x)                                                                                                                                                                                                        x*\-1 + e / *cos(x)                                                  /
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        64*x*cos(x)
x1−excos⁡(x)(−32(xexcos⁡(x)1−ex+21−ex(xsin⁡(x)−cos⁡(x)))sin⁡2(x)1−excos⁡2(x)−16(xexcos⁡(x)1−ex+21−ex(xsin⁡(x)−cos⁡(x)))1−ex−16(−2xexsin⁡(x)1−ex+2xexcos⁡(x)1−ex+xe2xcos⁡(x)(1−ex)32+41−ex(xcos⁡(x)+2sin⁡(x))−2(xsin⁡(x)−cos⁡(x))ex1−ex+2excos⁡(x)1−ex)sin⁡(x)1−excos⁡(x)+4(8xexsin⁡(x)1−ex+4xe2xsin⁡(x)(1−ex)32−6xe2xcos⁡(x)(1−ex)32−3xe3xcos⁡(x)(1−ex)52+81−ex(xsin⁡(x)−3cos⁡(x))+4(xsin⁡(x)−cos⁡(x))ex1−ex+8(xcos⁡(x)+2sin⁡(x))ex1−ex+8exsin⁡(x)1−ex−8excos⁡(x)1−ex+2(xsin⁡(x)−cos⁡(x))e2x(1−ex)32−4e2xcos⁡(x)(1−ex)32)1−ex−16(xexcos⁡(x)1−ex+21−ex(xsin⁡(x)−cos⁡(x)))exsin⁡(x)(1−ex)32cos⁡(x)−8(xexcos⁡(x)1−ex+21−ex(xsin⁡(x)−cos⁡(x)))ex(1−ex)32−8(−2xexsin⁡(x)1−ex+2xexcos⁡(x)1−ex+xe2xcos⁡(x)(1−ex)32+41−ex(xcos⁡(x)+2sin⁡(x))−2(xsin⁡(x)−cos⁡(x))ex1−ex+2excos⁡(x)1−ex)ex(1−ex)32−12(xexcos⁡(x)1−ex+21−ex(xsin⁡(x)−cos⁡(x)))e2x(1−ex)52−12(xexcos⁡(x)1−ex+21−ex(xsin⁡(x)−cos⁡(x)))(2x1−exsin⁡(x)+xexcos⁡(x)1−ex−21−excos⁡(x))sin⁡(x)x(ex−1)cos⁡2(x)−2(xexcos⁡(x)1−ex+21−ex(xsin⁡(x)−cos⁡(x)))(4x1−excos⁡(x)−4xexsin⁡(x)1−ex+2xexcos⁡(x)1−ex+xe2xcos⁡(x)(1−ex)32+81−exsin⁡(x)+4excos⁡(x)1−ex)x(ex−1)cos⁡(x)+6(xexcos⁡(x)1−ex+21−ex(xsin⁡(x)−cos⁡(x)))(2x1−exsin⁡(x)+xexcos⁡(x)1−ex−21−excos⁡(x))exx(ex−1)2cos⁡(x)−4(2x1−exsin⁡(x)+xexcos⁡(x)1−ex−21−excos⁡(x))(−2xexsin⁡(x)1−ex+2xexcos⁡(x)1−ex+xe2xcos⁡(x)(1−ex)32+41−ex(xcos⁡(x)+2sin⁡(x))−2(xsin⁡(x)−cos⁡(x))ex1−ex+2excos⁡(x)1−ex)x(ex−1)cos⁡(x)+32(xexcos⁡(x)1−ex+21−ex(xsin⁡(x)−cos⁡(x)))sin⁡(x)x1−excos⁡(x)+16(−2xexsin⁡(x)1−ex+2xexcos⁡(x)1−ex+xe2xcos⁡(x)(1−ex)32+41−ex(xcos⁡(x)+2sin⁡(x))−2(xsin⁡(x)−cos⁡(x))ex1−ex+2excos⁡(x)1−ex)x1−ex+16(xexcos⁡(x)1−ex+21−ex(xsin⁡(x)−cos⁡(x)))exx(1−ex)32+12(xexcos⁡(x)1−ex+21−ex(xsin⁡(x)−cos⁡(x)))(2x1−exsin⁡(x)+xexcos⁡(x)1−ex−21−excos⁡(x))x2(ex−1)cos⁡(x)−32(xexcos⁡(x)1−ex+21−ex(xsin⁡(x)−cos⁡(x)))x21−ex−(xexcos⁡(x)1−ex+21−ex(xsin⁡(x)−cos⁡(x)))(2x1−exsin⁡(x)+xexcos⁡(x)1−ex−21−excos⁡(x))2x2(1−ex)32cos⁡2(x))64xcos⁡(x)\frac{\sqrt{x \sqrt{1 - e^{x}} \cos{\left(x \right)}} \left(- \frac{32 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) \sin^{2}{\left(x \right)}}{\sqrt{1 - e^{x}} \cos^{2}{\left(x \right)}} - \frac{16 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right)}{\sqrt{1 - e^{x}}} - \frac{16 \left(- \frac{2 x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{2 x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{x e^{2 x} \cos{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + 4 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) - \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{2 e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}}\right) \sin{\left(x \right)}}{\sqrt{1 - e^{x}} \cos{\left(x \right)}} + \frac{4 \left(\frac{8 x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{4 x e^{2 x} \sin{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} - \frac{6 x e^{2 x} \cos{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} - \frac{3 x e^{3 x} \cos{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{5}{2}}} + 8 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - 3 \cos{\left(x \right)}\right) + \frac{4 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{8 \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{8 e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - \frac{8 e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) e^{2 x}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} - \frac{4 e^{2 x} \cos{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}}\right)}{\sqrt{1 - e^{x}}} - \frac{16 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) e^{x} \sin{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}} \cos{\left(x \right)}} - \frac{8 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) e^{x}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} - \frac{8 \left(- \frac{2 x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{2 x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{x e^{2 x} \cos{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + 4 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) - \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{2 e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}}\right) e^{x}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} - \frac{12 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) e^{2 x}}{\left(1 - e^{x}\right)^{\frac{5}{2}}} - \frac{12 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) \left(2 x \sqrt{1 - e^{x}} \sin{\left(x \right)} + \frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \cos{\left(x \right)}\right) \sin{\left(x \right)}}{x \left(e^{x} - 1\right) \cos^{2}{\left(x \right)}} - \frac{2 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) \left(4 x \sqrt{1 - e^{x}} \cos{\left(x \right)} - \frac{4 x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{2 x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{x e^{2 x} \cos{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + 8 \sqrt{1 - e^{x}} \sin{\left(x \right)} + \frac{4 e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}}\right)}{x \left(e^{x} - 1\right) \cos{\left(x \right)}} + \frac{6 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) \left(2 x \sqrt{1 - e^{x}} \sin{\left(x \right)} + \frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \cos{\left(x \right)}\right) e^{x}}{x \left(e^{x} - 1\right)^{2} \cos{\left(x \right)}} - \frac{4 \left(2 x \sqrt{1 - e^{x}} \sin{\left(x \right)} + \frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \cos{\left(x \right)}\right) \left(- \frac{2 x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{2 x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{x e^{2 x} \cos{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + 4 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) - \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{2 e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}}\right)}{x \left(e^{x} - 1\right) \cos{\left(x \right)}} + \frac{32 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) \sin{\left(x \right)}}{x \sqrt{1 - e^{x}} \cos{\left(x \right)}} + \frac{16 \left(- \frac{2 x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{2 x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{x e^{2 x} \cos{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + 4 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) - \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{2 e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}}\right)}{x \sqrt{1 - e^{x}}} + \frac{16 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) e^{x}}{x \left(1 - e^{x}\right)^{\frac{3}{2}}} + \frac{12 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) \left(2 x \sqrt{1 - e^{x}} \sin{\left(x \right)} + \frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \cos{\left(x \right)}\right)}{x^{2} \left(e^{x} - 1\right) \cos{\left(x \right)}} - \frac{32 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right)}{x^{2} \sqrt{1 - e^{x}}} - \frac{\left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) \left(2 x \sqrt{1 - e^{x}} \sin{\left(x \right)} + \frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \cos{\left(x \right)}\right)^{2}}{x^{2} \left(1 - e^{x}\right)^{\frac{3}{2}} \cos^{2}{\left(x \right)}}\right)}{64 x \cos{\left(x \right)}}
Simplificar
Gráfico
Derivada de y=sqrt(xcosxsqrt(1-e^x))
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