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√(xsinx√(1-e^x))
Derivada de la función/ 1-e^x/ xsinx/ √(xsinx√(1-e^x))

Derivada de √(xsinx√(1-e^x))

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

Gráfico:

interior superior

Definida a trozos:

Solución

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

  1. Sustituimos u=xsin⁡(x)1−exu = x \sin{\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 ddxxsin⁡(x)1−ex\frac{d}{d x} x \sin{\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)=xsin⁡(x)f{\left(x \right)} = x \sin{\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)=sin⁡(x)g{\left(x \right)} = \sin{\left(x \right)}; calculamos ddxg(x)\frac{d}{d x} g{\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: xcos⁡(x)+sin⁡(x)x \cos{\left(x \right)} + \sin{\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: −xexsin⁡(x)21−ex+1−ex(xcos⁡(x)+sin⁡(x))- \frac{x e^{x} \sin{\left(x \right)}}{2 \sqrt{1 - e^{x}}} + \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)

    Como resultado de la secuencia de reglas:

    −xexsin⁡(x)21−ex+1−ex(xcos⁡(x)+sin⁡(x))2x1−exsin⁡(x)\frac{- \frac{x e^{x} \sin{\left(x \right)}}{2 \sqrt{1 - e^{x}}} + \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{2 \sqrt{x \sqrt{1 - e^{x}} \sin{\left(x \right)}}}

  4. Simplificamos:

    −xexsin⁡(x)+2(1−ex)(xcos⁡(x)+sin⁡(x))4x1−exsin⁡(x)1−ex\frac{- x e^{x} \sin{\left(x \right)} + 2 \left(1 - e^{x}\right) \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{4 \sqrt{x \sqrt{1 - e^{x}} \sin{\left(x \right)}} \sqrt{1 - e^{x}}}

Respuesta:

−xexsin⁡(x)+2(1−ex)(xcos⁡(x)+sin⁡(x))4x1−exsin⁡(x)1−ex\frac{- x e^{x} \sin{\left(x \right)} + 2 \left(1 - e^{x}\right) \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{4 \sqrt{x \sqrt{1 - e^{x}} \sin{\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] 
    ______________________ /   ________                                    \
   /      ________         |  /      x                            x        |
  /      /      x          |\/  1 - E  *(x*cos(x) + sin(x))    x*e *sin(x) |
\/   x*\/  1 - E  *sin(x) *|------------------------------- - -------------|
                           |               2                       ________|
                           |                                      /      x |
                           \                                  4*\/  1 - E  /
----------------------------------------------------------------------------
                                 ________                                   
                                /      x                                    
                            x*\/  1 - E  *sin(x)
x1−exsin⁡(x)(−xexsin⁡(x)41−ex+1−ex(xcos⁡(x)+sin⁡(x))2)x1−exsin⁡(x)\frac{\sqrt{x \sqrt{1 - e^{x}} \sin{\left(x \right)}} \left(- \frac{x e^{x} \sin{\left(x \right)}}{4 \sqrt{1 - e^{x}}} + \frac{\sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{2}\right)}{x \sqrt{1 - e^{x}} \sin{\left(x \right)}}
Simplificar
Segunda derivada [src] 
                           /    /     ________                                                 x      x             2*x                      x        x       \     /       ________                          x       \        /       ________                          x       \     /       ________                          x       \          /       ________                          x       \ /     ________                 ________             x       \\
                           |    |    /      x                           2*(x*cos(x) + sin(x))*e    2*e *sin(x)   x*e   *sin(x)   2*x*cos(x)*e    2*x*e *sin(x)|     |      /      x                        x*e *sin(x)|  x     |      /      x                        x*e *sin(x)|     |      /      x                        x*e *sin(x)|          |      /      x                        x*e *sin(x)| |    /      x                 /      x           x*e *sin(x)||
                           |  2*|4*\/  1 - e  *(-2*cos(x) + x*sin(x)) + ------------------------ + ----------- + ------------- + ------------- + -------------|   2*|- 2*\/  1 - e  *(x*cos(x) + sin(x)) + -----------|*e    4*|- 2*\/  1 - e  *(x*cos(x) + sin(x)) + -----------|   4*|- 2*\/  1 - e  *(x*cos(x) + sin(x)) + -----------|*cos(x)   |- 2*\/  1 - e  *(x*cos(x) + sin(x)) + -----------|*|2*\/  1 - e  *sin(x) + 2*x*\/  1 - e  *cos(x) - -----------||
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  /      /      x          |    \                                             \/  1 - e            \/  1 - e      \1 - e /        \/  1 - e       \/  1 - e   /     \                                      \/  1 - e  /        \                                      \/  1 - e  /     \                                      \/  1 - e  /          \                                      \/  1 - e  / \                                                \/  1 - e  /|
\/   x*\/  1 - e  *sin(x) *|- --------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------- + ----------------------------------------------------- + ------------------------------------------------------------ + -----------------------------------------------------------------------------------------------------------------|
                           |                                                                ________                                                                                            3/2                                                   ________                                               ________                                                                                 /      x\                                                      |
                           |                                                               /      x                                                                                     /     x\                                                     /      x                                               /      x                                                                                x*\-1 + e /*sin(x)                                               |
                           \                                                             \/  1 - e                                                                                      \1 - e /                                                 x*\/  1 - e                                              \/  1 - e  *sin(x)                                                                                                                                         /
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                                                                                                                                                                                                                             16*x*sin(x)
x1−exsin⁡(x)(4(xexsin⁡(x)1−ex−21−ex(xcos⁡(x)+sin⁡(x)))cos⁡(x)1−exsin⁡(x)−2(2xexsin⁡(x)1−ex+2xexcos⁡(x)1−ex+xe2xsin⁡(x)(1−ex)32+41−ex(xsin⁡(x)−2cos⁡(x))+2(xcos⁡(x)+sin⁡(x))ex1−ex+2exsin⁡(x)1−ex)1−ex−2(xexsin⁡(x)1−ex−21−ex(xcos⁡(x)+sin⁡(x)))ex(1−ex)32+(xexsin⁡(x)1−ex−21−ex(xcos⁡(x)+sin⁡(x)))(2x1−excos⁡(x)−xexsin⁡(x)1−ex+21−exsin⁡(x))x(ex−1)sin⁡(x)+4(xexsin⁡(x)1−ex−21−ex(xcos⁡(x)+sin⁡(x)))x1−ex)16xsin⁡(x)\frac{\sqrt{x \sqrt{1 - e^{x}} \sin{\left(x \right)}} \left(\frac{4 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) \cos{\left(x \right)}}{\sqrt{1 - e^{x}} \sin{\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} \sin{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + 4 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{2 e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}}\right)}{\sqrt{1 - e^{x}}} - \frac{2 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) e^{x}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + \frac{\left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) \left(2 x \sqrt{1 - e^{x}} \cos{\left(x \right)} - \frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \sin{\left(x \right)}\right)}{x \left(e^{x} - 1\right) \sin{\left(x \right)}} + \frac{4 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right)}{x \sqrt{1 - e^{x}}}\right)}{16 x \sin{\left(x \right)}}
Simplificar
Tercera derivada [src] 
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                           |     /       ________                          x       \     /     ________                                                   x                          2*x      2*x                                 x             x      x               3*x                      2*x        2*x                      x\      /       ________                          x       \      /       ________                          x       \          /       ________                          x       \        /     ________                                                 x      x             2*x                      x        x       \         /     ________                                                 x      x             2*x                      x        x       \              /       ________                          x       \      /       ________                          x       \         /     ________                                                 x      x             2*x                      x        x       \          /     ________                 ________             x       \  /       ________                          x       \      /       ________                          x       \             /       ________                          x       \ /     ________                 ________             x       \     /       ________                          x       \ /       ________                 ________             x             2*x               x                      x\     /     ________                 ________             x       \ /     ________                                                 x      x             2*x                      x        x       \      /       ________                          x       \                /       ________                          x       \ /     ________                 ________             x       \            /       ________                          x       \ /     ________                 ________             x       \   |
                           |     |      /      x                        x*e *sin(x)|     |    /      x                          8*(-2*cos(x) + x*sin(x))*e    2*(x*cos(x) + sin(x))*e      4*e   *sin(x)   4*(x*cos(x) + sin(x))*e    8*cos(x)*e    8*e *sin(x)   3*x*e   *sin(x)   4*x*cos(x)*e      6*x*e   *sin(x)   8*x*cos(x)*e |      |      /      x                        x*e *sin(x)|      |      /      x                        x*e *sin(x)|  2*x     |      /      x                        x*e *sin(x)|  x     |    /      x                           2*(x*cos(x) + sin(x))*e    2*e *sin(x)   x*e   *sin(x)   2*x*cos(x)*e    2*x*e *sin(x)|  x      |    /      x                           2*(x*cos(x) + sin(x))*e    2*e *sin(x)   x*e   *sin(x)   2*x*cos(x)*e    2*x*e *sin(x)|         2    |      /      x                        x*e *sin(x)|      |      /      x                        x*e *sin(x)|  x      |    /      x                           2*(x*cos(x) + sin(x))*e    2*e *sin(x)   x*e   *sin(x)   2*x*cos(x)*e    2*x*e *sin(x)|          |    /      x                 /      x           x*e *sin(x)|  |      /      x                        x*e *sin(x)|      |      /      x                        x*e *sin(x)|             |      /      x                        x*e *sin(x)| |    /      x                 /      x           x*e *sin(x)|     |      /      x                        x*e *sin(x)| |      /      x                 /      x           4*e *sin(x)   x*e   *sin(x)   2*x*e *sin(x)   4*x*cos(x)*e |     |    /      x                 /      x           x*e *sin(x)| |    /      x                           2*(x*cos(x) + sin(x))*e    2*e *sin(x)   x*e   *sin(x)   2*x*cos(x)*e    2*x*e *sin(x)|      |      /      x                        x*e *sin(x)|         x      |      /      x                        x*e *sin(x)| |    /      x                 /      x           x*e *sin(x)|            |      /      x                        x*e *sin(x)| |    /      x                 /      x           x*e *sin(x)|  x|
                           |  16*|- 2*\/  1 - e  *(x*cos(x) + sin(x)) + -----------|   4*|8*\/  1 - e  *(3*sin(x) + x*cos(x)) - --------------------------- + -------------------------- + ------------- + ------------------------ + ----------- + ----------- + --------------- + --------------- + --------------- + -------------|   32*|- 2*\/  1 - e  *(x*cos(x) + sin(x)) + -----------|   12*|- 2*\/  1 - e  *(x*cos(x) + sin(x)) + -----------|*e      8*|- 2*\/  1 - e  *(x*cos(x) + sin(x)) + -----------|*e    8*|4*\/  1 - e  *(-2*cos(x) + x*sin(x)) + ------------------------ + ----------- + ------------- + ------------- + -------------|*e    16*|4*\/  1 - e  *(-2*cos(x) + x*sin(x)) + ------------------------ + ----------- + ------------- + ------------- + -------------|   32*cos (x)*|- 2*\/  1 - e  *(x*cos(x) + sin(x)) + -----------|   16*|- 2*\/  1 - e  *(x*cos(x) + sin(x)) + -----------|*e    16*|4*\/  1 - e  *(-2*cos(x) + x*sin(x)) + ------------------------ + ----------- + ------------- + ------------- + -------------|*cos(x)   |2*\/  1 - e  *sin(x) + 2*x*\/  1 - e  *cos(x) - -----------| *|- 2*\/  1 - e  *(x*cos(x) + sin(x)) + -----------|   32*|- 2*\/  1 - e  *(x*cos(x) + sin(x)) + -----------|*cos(x)   12*|- 2*\/  1 - e  *(x*cos(x) + sin(x)) + -----------|*|2*\/  1 - e  *sin(x) + 2*x*\/  1 - e  *cos(x) - -----------|   2*|- 2*\/  1 - e  *(x*cos(x) + sin(x)) + -----------|*|- 8*\/  1 - e  *cos(x) + 4*x*\/  1 - e  *sin(x) + ----------- + ------------- + ------------- + -------------|   4*|2*\/  1 - e  *sin(x) + 2*x*\/  1 - e  *cos(x) - -----------|*|4*\/  1 - e  *(-2*cos(x) + x*sin(x)) + ------------------------ + ----------- + ------------- + ------------- + -------------|   16*|- 2*\/  1 - e  *(x*cos(x) + sin(x)) + -----------|*cos(x)*e    12*|- 2*\/  1 - e  *(x*cos(x) + sin(x)) + -----------|*|2*\/  1 - e  *sin(x) + 2*x*\/  1 - e  *cos(x) - -----------|*cos(x)   6*|- 2*\/  1 - e  *(x*cos(x) + sin(x)) + -----------|*|2*\/  1 - e  *sin(x) + 2*x*\/  1 - e  *cos(x) - -----------|*e |
    ______________________ |     |                                         ________|     |                                                 ________                          3/2                    3/2             ________             ________      ________             5/2               3/2               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  *sin(x) *|- ------------------------------------------------------ - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------ - ----------------------------------------------------------- - -------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------- + --------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------|
                           |                          ________                                                                                                                                              ________                                                                                                                                               ________                                                       5/2                                                         3/2                                                                                              3/2                                                                                                                               ________                                                                                      ________                                                                 3/2                                                                                        ________                                                                                                                              3/2                                                                                   ________                                                                               2 /      x\                                                                                                                                       /      x\                                                                                                                                                                            /      x\                                                                                                                               3/2                                                                                       /      x\    2                                                                                                                      2                                                         |
                           |                         /      x                                                                                                                                              /      x                                                                                                                                           2   /      x                                                /     x\                                                    /     x\                                                                                         /     x\                                                                                                                                 /      x                                                                                      /      x     2                                                    /     x\                                                                                          /      x                                                                                                                     2 /     x\       2                                                                             /      x                                                                               x *\-1 + e /*sin(x)                                                                                                                              x*\-1 + e /*sin(x)                                                                                                                                                                   x*\-1 + e /*sin(x)                                                                                                                /     x\                                                                                        x*\-1 + e /*sin (x)                                                                                                          /      x\                                                          |
                           \                       \/  1 - e                                                                                                                                             \/  1 - e                                                                                                                                           x *\/  1 - e                                                 \1 - e /                                                    \1 - e /                                                                                         \1 - e /                                                                                                                             x*\/  1 - e                                                                                     \/  1 - e  *sin (x)                                               x*\1 - e /                                                                                        \/  1 - e  *sin(x)                                                                                                            x *\1 - e /   *sin (x)                                                                      x*\/  1 - e  *sin(x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               \1 - e /   *sin(x)                                                                                                                                                                                                         x*\-1 + e / *sin(x)                                                  /
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         64*x*sin(x)
x1−exsin⁡(x)(−16(xexsin⁡(x)1−ex−21−ex(xcos⁡(x)+sin⁡(x)))1−ex−32(xexsin⁡(x)1−ex−21−ex(xcos⁡(x)+sin⁡(x)))cos⁡2(x)1−exsin⁡2(x)+16(2xexsin⁡(x)1−ex+2xexcos⁡(x)1−ex+xe2xsin⁡(x)(1−ex)32+41−ex(xsin⁡(x)−2cos⁡(x))+2(xcos⁡(x)+sin⁡(x))ex1−ex+2exsin⁡(x)1−ex)cos⁡(x)1−exsin⁡(x)−4(8xexcos⁡(x)1−ex+6xe2xsin⁡(x)(1−ex)32+4xe2xcos⁡(x)(1−ex)32+3xe3xsin⁡(x)(1−ex)52+81−ex(xcos⁡(x)+3sin⁡(x))−8(xsin⁡(x)−2cos⁡(x))ex1−ex+4(xcos⁡(x)+sin⁡(x))ex1−ex+8exsin⁡(x)1−ex+8excos⁡(x)1−ex+2(xcos⁡(x)+sin⁡(x))e2x(1−ex)32+4e2xsin⁡(x)(1−ex)32)1−ex−8(xexsin⁡(x)1−ex−21−ex(xcos⁡(x)+sin⁡(x)))ex(1−ex)32+16(xexsin⁡(x)1−ex−21−ex(xcos⁡(x)+sin⁡(x)))excos⁡(x)(1−ex)32sin⁡(x)−8(2xexsin⁡(x)1−ex+2xexcos⁡(x)1−ex+xe2xsin⁡(x)(1−ex)32+41−ex(xsin⁡(x)−2cos⁡(x))+2(xcos⁡(x)+sin⁡(x))ex1−ex+2exsin⁡(x)1−ex)ex(1−ex)32−12(xexsin⁡(x)1−ex−21−ex(xcos⁡(x)+sin⁡(x)))e2x(1−ex)52−12(xexsin⁡(x)1−ex−21−ex(xcos⁡(x)+sin⁡(x)))(2x1−excos⁡(x)−xexsin⁡(x)1−ex+21−exsin⁡(x))cos⁡(x)x(ex−1)sin⁡2(x)−2(xexsin⁡(x)1−ex−21−ex(xcos⁡(x)+sin⁡(x)))(4x1−exsin⁡(x)+2xexsin⁡(x)1−ex+4xexcos⁡(x)1−ex+xe2xsin⁡(x)(1−ex)32−81−excos⁡(x)+4exsin⁡(x)1−ex)x(ex−1)sin⁡(x)−6(xexsin⁡(x)1−ex−21−ex(xcos⁡(x)+sin⁡(x)))(2x1−excos⁡(x)−xexsin⁡(x)1−ex+21−exsin⁡(x))exx(ex−1)2sin⁡(x)+4(2x1−excos⁡(x)−xexsin⁡(x)1−ex+21−exsin⁡(x))(2xexsin⁡(x)1−ex+2xexcos⁡(x)1−ex+xe2xsin⁡(x)(1−ex)32+41−ex(xsin⁡(x)−2cos⁡(x))+2(xcos⁡(x)+sin⁡(x))ex1−ex+2exsin⁡(x)1−ex)x(ex−1)sin⁡(x)−32(xexsin⁡(x)1−ex−21−ex(xcos⁡(x)+sin⁡(x)))cos⁡(x)x1−exsin⁡(x)+16(2xexsin⁡(x)1−ex+2xexcos⁡(x)1−ex+xe2xsin⁡(x)(1−ex)32+41−ex(xsin⁡(x)−2cos⁡(x))+2(xcos⁡(x)+sin⁡(x))ex1−ex+2exsin⁡(x)1−ex)x1−ex+16(xexsin⁡(x)1−ex−21−ex(xcos⁡(x)+sin⁡(x)))exx(1−ex)32−12(xexsin⁡(x)1−ex−21−ex(xcos⁡(x)+sin⁡(x)))(2x1−excos⁡(x)−xexsin⁡(x)1−ex+21−exsin⁡(x))x2(ex−1)sin⁡(x)−32(xexsin⁡(x)1−ex−21−ex(xcos⁡(x)+sin⁡(x)))x21−ex−(xexsin⁡(x)1−ex−21−ex(xcos⁡(x)+sin⁡(x)))(2x1−excos⁡(x)−xexsin⁡(x)1−ex+21−exsin⁡(x))2x2(1−ex)32sin⁡2(x))64xsin⁡(x)\frac{\sqrt{x \sqrt{1 - e^{x}} \sin{\left(x \right)}} \left(- \frac{16 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right)}{\sqrt{1 - e^{x}}} - \frac{32 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) \cos^{2}{\left(x \right)}}{\sqrt{1 - e^{x}} \sin^{2}{\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} \sin{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + 4 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{2 e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}}\right) \cos{\left(x \right)}}{\sqrt{1 - e^{x}} \sin{\left(x \right)}} - \frac{4 \left(\frac{8 x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{6 x e^{2 x} \sin{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + \frac{4 x e^{2 x} \cos{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + \frac{3 x e^{3 x} \sin{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{5}{2}}} + 8 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + 3 \sin{\left(x \right)}\right) - \frac{8 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{4 \left(x \cos{\left(x \right)} + \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 \cos{\left(x \right)} + \sin{\left(x \right)}\right) e^{2 x}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + \frac{4 e^{2 x} \sin{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}}\right)}{\sqrt{1 - e^{x}}} - \frac{8 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) e^{x}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + \frac{16 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) e^{x} \cos{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}} \sin{\left(x \right)}} - \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} \sin{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + 4 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{2 e^{x} \sin{\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} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) e^{2 x}}{\left(1 - e^{x}\right)^{\frac{5}{2}}} - \frac{12 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) \left(2 x \sqrt{1 - e^{x}} \cos{\left(x \right)} - \frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \sin{\left(x \right)}\right) \cos{\left(x \right)}}{x \left(e^{x} - 1\right) \sin^{2}{\left(x \right)}} - \frac{2 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) \left(4 x \sqrt{1 - e^{x}} \sin{\left(x \right)} + \frac{2 x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{4 x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{x e^{2 x} \sin{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} - 8 \sqrt{1 - e^{x}} \cos{\left(x \right)} + \frac{4 e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}}\right)}{x \left(e^{x} - 1\right) \sin{\left(x \right)}} - \frac{6 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) \left(2 x \sqrt{1 - e^{x}} \cos{\left(x \right)} - \frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \sin{\left(x \right)}\right) e^{x}}{x \left(e^{x} - 1\right)^{2} \sin{\left(x \right)}} + \frac{4 \left(2 x \sqrt{1 - e^{x}} \cos{\left(x \right)} - \frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \sin{\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} \sin{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + 4 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{2 e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}}\right)}{x \left(e^{x} - 1\right) \sin{\left(x \right)}} - \frac{32 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) \cos{\left(x \right)}}{x \sqrt{1 - e^{x}} \sin{\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} \sin{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + 4 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{2 e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}}\right)}{x \sqrt{1 - e^{x}}} + \frac{16 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) e^{x}}{x \left(1 - e^{x}\right)^{\frac{3}{2}}} - \frac{12 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) \left(2 x \sqrt{1 - e^{x}} \cos{\left(x \right)} - \frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \sin{\left(x \right)}\right)}{x^{2} \left(e^{x} - 1\right) \sin{\left(x \right)}} - \frac{32 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right)}{x^{2} \sqrt{1 - e^{x}}} - \frac{\left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) \left(2 x \sqrt{1 - e^{x}} \cos{\left(x \right)} - \frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \sin{\left(x \right)}\right)^{2}}{x^{2} \left(1 - e^{x}\right)^{\frac{3}{2}} \sin^{2}{\left(x \right)}}\right)}{64 x \sin{\left(x \right)}}
Simplificar
Gráfico
Derivada de √(xsinx√(1-e^x))
    © Sr Examen – Калькулятор