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Derivada de la función/ x*sin/ ln(x)/ 2^2^x/ sin(x)/ (x*sin(x))^(ln(x)*2^2^x)

Derivada de (x*sin(x))^(ln(x)*2^2^x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
                  / x\
                  \2 /
          log(x)*2    
(x*sin(x))
(xsin⁡(x))22xlog⁡(x)\left(x \sin{\left(x \right)}\right)^{2^{2^{x}} \log{\left(x \right)}} 
(x*sin(x))^(log(x)*2^(2^x))
Solución detallada

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

    Perola derivada

    (22xlog⁡(x))22xlog⁡(x)(log⁡(22xlog⁡(x))+1)\left(2^{2^{x}} \log{\left(x \right)}\right)^{2^{2^{x}} \log{\left(x \right)}} \left(\log{\left(2^{2^{x}} \log{\left(x \right)} \right)} + 1\right)

  2. Simplificamos:

    (22xlog⁡(x))22xlog⁡(x)(log⁡(22xlog⁡(x))+1)\left(2^{2^{x}} \log{\left(x \right)}\right)^{2^{2^{x}} \log{\left(x \right)}} \left(\log{\left(2^{2^{x}} \log{\left(x \right)} \right)} + 1\right)

Respuesta:

(22xlog⁡(x))22xlog⁡(x)(log⁡(22xlog⁡(x))+1)\left(2^{2^{x}} \log{\left(x \right)}\right)^{2^{2^{x}} \log{\left(x \right)}} \left(\log{\left(2^{2^{x}} \log{\left(x \right)} \right)} + 1\right)

Primera derivada [src] 
                  / x\ // / x\                          \                  / x\                           \
                  \2 / || \2 /       / x\               |                  \2 /                           |
          log(x)*2     ||2        x  \2 /    2          |                 2    *(x*cos(x) + sin(x))*log(x)|
(x*sin(x))            *||----- + 2 *2    *log (2)*log(x)|*log(x*sin(x)) + --------------------------------|
                       \\  x                            /                             x*sin(x)            /
(xsin⁡(x))22xlog⁡(x)(22x(xcos⁡(x)+sin⁡(x))log⁡(x)xsin⁡(x)+(22x2xlog⁡(2)2log⁡(x)+22xx)log⁡(xsin⁡(x)))\left(x \sin{\left(x \right)}\right)^{2^{2^{x}} \log{\left(x \right)}} \left(\frac{2^{2^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{x \sin{\left(x \right)}} + \left(2^{2^{x}} 2^{x} \log{\left(2 \right)}^{2} \log{\left(x \right)} + \frac{2^{2^{x}}}{x}\right) \log{\left(x \sin{\left(x \right)} \right)}\right)
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Segunda derivada [src] 
                 / x\        /                                                                                                                                                                                  /1    x    2          \                                                                                                                                                             \
 / x\            \2 /        | / x\                                                                     2   /                                                    x    2   \                                     |- + 2 *log (2)*log(x)|*(x*cos(x) + sin(x))                                                                                                     x    2                              |
 \2 /           2    *log(x) | \2 / //1    x    2          \                 (x*cos(x) + sin(x))*log(x)\    |  1     x    3              2*x    4             2*2 *log (2)|                 x*cos(x) + sin(x)   \x                    /                       (-2*cos(x) + x*sin(x))*log(x)   (x*cos(x) + sin(x))*log(x)   (x*cos(x) + sin(x))*cos(x)*log(x)   2 *log (2)*(x*cos(x) + sin(x))*log(x)|
2    *(x*sin(x))            *|2    *||- + 2 *log (2)*log(x)|*log(x*sin(x)) + --------------------------|  + |- -- + 2 *log (2)*log(x) + 2   *log (2)*log(x) + ------------|*log(x*sin(x)) + ----------------- + ------------------------------------------- - ----------------------------- - -------------------------- - --------------------------------- + -------------------------------------|
                             |      \\x                    /                          x*sin(x)         /    |   2                                                  x      |                      2                                x*sin(x)                               x*sin(x)                      2                                    2                                 x*sin(x)              |
                             \                                                                              \  x                                                          /                     x *sin(x)                                                                                             x *sin(x)                        x*sin (x)                                                    /
22x(xsin⁡(x))22xlog⁡(x)(22x((2xlog⁡(2)2log⁡(x)+1x)log⁡(xsin⁡(x))+(xcos⁡(x)+sin⁡(x))log⁡(x)xsin⁡(x))2+2x(xcos⁡(x)+sin⁡(x))log⁡(2)2log⁡(x)xsin⁡(x)+(22xlog⁡(2)4log⁡(x)+2xlog⁡(2)3log⁡(x)+2⋅2xlog⁡(2)2x−1x2)log⁡(xsin⁡(x))−(xsin⁡(x)−2cos⁡(x))log⁡(x)xsin⁡(x)+(xcos⁡(x)+sin⁡(x))(2xlog⁡(2)2log⁡(x)+1x)xsin⁡(x)−(xcos⁡(x)+sin⁡(x))log⁡(x)cos⁡(x)xsin⁡2(x)−(xcos⁡(x)+sin⁡(x))log⁡(x)x2sin⁡(x)+xcos⁡(x)+sin⁡(x)x2sin⁡(x))2^{2^{x}} \left(x \sin{\left(x \right)}\right)^{2^{2^{x}} \log{\left(x \right)}} \left(2^{2^{x}} \left(\left(2^{x} \log{\left(2 \right)}^{2} \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \sin{\left(x \right)} \right)} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{x \sin{\left(x \right)}}\right)^{2} + \frac{2^{x} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(2 \right)}^{2} \log{\left(x \right)}}{x \sin{\left(x \right)}} + \left(2^{2 x} \log{\left(2 \right)}^{4} \log{\left(x \right)} + 2^{x} \log{\left(2 \right)}^{3} \log{\left(x \right)} + \frac{2 \cdot 2^{x} \log{\left(2 \right)}^{2}}{x} - \frac{1}{x^{2}}\right) \log{\left(x \sin{\left(x \right)} \right)} - \frac{\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x \right)}}{x \sin{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(2^{x} \log{\left(2 \right)}^{2} \log{\left(x \right)} + \frac{1}{x}\right)}{x \sin{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)} \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{x^{2} \sin{\left(x \right)}} + \frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{x^{2} \sin{\left(x \right)}}\right)
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Tercera derivada [src] 
                             /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 /                                                    x    2   \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         \
                             |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 |  1     x    3              2*x    4             2*2 *log (2)|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |
                 / x\        |                                                                                                                                                                                                                                                                                                                                                    /                                                                                                    /1    x    2          \                                                                                                                                                             \                                /1    x    2          \                                                         /1    x    2          \                                                      2*(x*cos(x) + sin(x))*|- -- + 2 *log (2)*log(x) + 2   *log (2)*log(x) + ------------|                                                                    /1    x    2          \                                                                                                                                                                                                                                                                                                                                                                                                              |
 / x\            \2 /        |    x                                                                     3   /                                                  x    2         x    3         2*x    4                           \                                                                       / x\                                                                      |/                                                    x    2   \                                     |- + 2 *log (2)*log(x)|*(x*cos(x) + sin(x))                                                                                                     x    2                              |                                |- + 2 *log (2)*log(x)|*(-2*cos(x) + x*sin(x))                                  |- + 2 *log (2)*log(x)|*(x*cos(x) + sin(x))                                                        |   2                                                  x      |                                                                    |- + 2 *log (2)*log(x)|*(x*cos(x) + sin(x))*cos(x)      x    2                               2                                                                                                                 x    3                                  2*x    4                                    x    2                                       x    2                                    x    2                                     |
 \2 /           2    *log(x) | 2*2  //1    x    2          \                 (x*cos(x) + sin(x))*log(x)\    |2     x    4              3*x    6             3*2 *log (2)   3*2 *log (2)   3*2   *log (2)      2*x    5          |                 3*(x*cos(x) + sin(x))   2*(-2*cos(x) + x*sin(x))      \2 / //1    x    2          \                 (x*cos(x) + sin(x))*log(x)\ ||  1     x    3              2*x    4             2*2 *log (2)|                 x*cos(x) + sin(x)   \x                    /                       (-2*cos(x) + x*sin(x))*log(x)   (x*cos(x) + sin(x))*log(x)   (x*cos(x) + sin(x))*cos(x)*log(x)   2 *log (2)*(x*cos(x) + sin(x))*log(x)|   (x*cos(x) + sin(x))*log(x)   \x                    /                          (3*sin(x) + x*cos(x))*log(x)   \x                    /                       2*(x*cos(x) + sin(x))*cos(x)                         \  x                                                          /   2*(x*cos(x) + sin(x))*log(x)   2*(-2*cos(x) + x*sin(x))*log(x)   \x                    /                              2*2 *log (2)*(x*cos(x) + sin(x))   2*cos (x)*(x*cos(x) + sin(x))*log(x)   2*(-2*cos(x) + x*sin(x))*cos(x)*log(x)   2*(x*cos(x) + sin(x))*cos(x)*log(x)   2 *log (2)*(x*cos(x) + sin(x))*log(x)   2   *log (2)*(x*cos(x) + sin(x))*log(x)   2*2 *log (2)*(-2*cos(x) + x*sin(x))*log(x)   2*2 *log (2)*(x*cos(x) + sin(x))*log(x)   2*2 *log (2)*(x*cos(x) + sin(x))*cos(x)*log(x)|
2    *(x*sin(x))            *|2    *||- + 2 *log (2)*log(x)|*log(x*sin(x)) + --------------------------|  + |-- + 2 *log (2)*log(x) + 2   *log (2)*log(x) - ------------ + ------------ + -------------- + 3*2   *log (2)*log(x)|*log(x*sin(x)) - --------------------- - ------------------------ + 3*2    *||- + 2 *log (2)*log(x)|*log(x*sin(x)) + --------------------------|*||- -- + 2 *log (2)*log(x) + 2   *log (2)*log(x) + ------------|*log(x*sin(x)) + ----------------- + ------------------------------------------- - ----------------------------- - -------------------------- - --------------------------------- + -------------------------------------| + -------------------------- - ---------------------------------------------- - ---------------------------- - ------------------------------------------- - ---------------------------- + ------------------------------------------------------------------------------------- + ---------------------------- + ------------------------------- - -------------------------------------------------- + -------------------------------- + ------------------------------------ + -------------------------------------- + ----------------------------------- + ------------------------------------- + --------------------------------------- - ------------------------------------------ - --------------------------------------- - ----------------------------------------------|
                             |      \\x                    /                          x*sin(x)         /    | 3                                                   2             x               x                               |                        3                        2                          \\x                    /                          x*sin(x)         / ||   2                                                  x      |                      2                                x*sin(x)                               x*sin(x)                      2                                    2                                 x*sin(x)              |            x*sin(x)                               x*sin(x)                                x*sin(x)                               2                                     2    2                                                      x*sin(x)                                                   3                                2                                              2                                       2                                        3                                       2                                   2    2                                 x*sin(x)                                 x*sin(x)                                   x*sin(x)                                    2                                                2                      |
                             \                                                                              \x                                                   x                                                              /                       x *sin(x)                x *sin(x)                                                                                        \\  x                                                          /                     x *sin(x)                                                                                             x *sin(x)                        x*sin (x)                                                    /                                                                                                                                 x *sin(x)                             x *sin (x)                                                                                                             x *sin(x)                        x *sin(x)                                  x*sin (x)                                   x *sin(x)                            x*sin (x)                               x*sin (x)                               x *sin (x)                                                                                                                                                             x *sin(x)                                    x*sin (x)                   /
22x(xsin⁡(x))22xlog⁡(x)(22⋅2x((2xlog⁡(2)2log⁡(x)+1x)log⁡(xsin⁡(x))+(xcos⁡(x)+sin⁡(x))log⁡(x)xsin⁡(x))3+3⋅22x((2xlog⁡(2)2log⁡(x)+1x)log⁡(xsin⁡(x))+(xcos⁡(x)+sin⁡(x))log⁡(x)xsin⁡(x))(2x(xcos⁡(x)+sin⁡(x))log⁡(2)2log⁡(x)xsin⁡(x)+(22xlog⁡(2)4log⁡(x)+2xlog⁡(2)3log⁡(x)+2⋅2xlog⁡(2)2x−1x2)log⁡(xsin⁡(x))−(xsin⁡(x)−2cos⁡(x))log⁡(x)xsin⁡(x)+(xcos⁡(x)+sin⁡(x))(2xlog⁡(2)2log⁡(x)+1x)xsin⁡(x)−(xcos⁡(x)+sin⁡(x))log⁡(x)cos⁡(x)xsin⁡2(x)−(xcos⁡(x)+sin⁡(x))log⁡(x)x2sin⁡(x)+xcos⁡(x)+sin⁡(x)x2sin⁡(x))+22x(xcos⁡(x)+sin⁡(x))log⁡(2)4log⁡(x)xsin⁡(x)−2⋅2x(xsin⁡(x)−2cos⁡(x))log⁡(2)2log⁡(x)xsin⁡(x)+2x(xcos⁡(x)+sin⁡(x))log⁡(2)3log⁡(x)xsin⁡(x)−2⋅2x(xcos⁡(x)+sin⁡(x))log⁡(2)2log⁡(x)cos⁡(x)xsin⁡2(x)−2⋅2x(xcos⁡(x)+sin⁡(x))log⁡(2)2log⁡(x)x2sin⁡(x)+2⋅2x(xcos⁡(x)+sin⁡(x))log⁡(2)2x2sin⁡(x)+(23xlog⁡(2)6log⁡(x)+3⋅22xlog⁡(2)5log⁡(x)+3⋅22xlog⁡(2)4x+2xlog⁡(2)4log⁡(x)+3⋅2xlog⁡(2)3x−3⋅2xlog⁡(2)2x2+2x3)log⁡(xsin⁡(x))−(xsin⁡(x)−2cos⁡(x))(2xlog⁡(2)2log⁡(x)+1x)xsin⁡(x)+2(xsin⁡(x)−2cos⁡(x))log⁡(x)cos⁡(x)xsin⁡2(x)−(xcos⁡(x)+sin⁡(x))(2xlog⁡(2)2log⁡(x)+1x)cos⁡(x)xsin⁡2(x)+2(xcos⁡(x)+sin⁡(x))(22xlog⁡(2)4log⁡(x)+2xlog⁡(2)3log⁡(x)+2⋅2xlog⁡(2)2x−1x2)xsin⁡(x)+(xcos⁡(x)+sin⁡(x))log⁡(x)xsin⁡(x)+2(xcos⁡(x)+sin⁡(x))log⁡(x)cos⁡2(x)xsin⁡3(x)−(xcos⁡(x)+3sin⁡(x))log⁡(x)xsin⁡(x)+2(xsin⁡(x)−2cos⁡(x))log⁡(x)x2sin⁡(x)−2(xsin⁡(x)−2cos⁡(x))x2sin⁡(x)−(xcos⁡(x)+sin⁡(x))(2xlog⁡(2)2log⁡(x)+1x)x2sin⁡(x)+2(xcos⁡(x)+sin⁡(x))log⁡(x)cos⁡(x)x2sin⁡2(x)−2(xcos⁡(x)+sin⁡(x))cos⁡(x)x2sin⁡2(x)+2(xcos⁡(x)+sin⁡(x))log⁡(x)x3sin⁡(x)−3(xcos⁡(x)+sin⁡(x))x3sin⁡(x))2^{2^{x}} \left(x \sin{\left(x \right)}\right)^{2^{2^{x}} \log{\left(x \right)}} \left(2^{2 \cdot 2^{x}} \left(\left(2^{x} \log{\left(2 \right)}^{2} \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \sin{\left(x \right)} \right)} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{x \sin{\left(x \right)}}\right)^{3} + 3 \cdot 2^{2^{x}} \left(\left(2^{x} \log{\left(2 \right)}^{2} \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(x \sin{\left(x \right)} \right)} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{x \sin{\left(x \right)}}\right) \left(\frac{2^{x} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(2 \right)}^{2} \log{\left(x \right)}}{x \sin{\left(x \right)}} + \left(2^{2 x} \log{\left(2 \right)}^{4} \log{\left(x \right)} + 2^{x} \log{\left(2 \right)}^{3} \log{\left(x \right)} + \frac{2 \cdot 2^{x} \log{\left(2 \right)}^{2}}{x} - \frac{1}{x^{2}}\right) \log{\left(x \sin{\left(x \right)} \right)} - \frac{\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x \right)}}{x \sin{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(2^{x} \log{\left(2 \right)}^{2} \log{\left(x \right)} + \frac{1}{x}\right)}{x \sin{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)} \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{x^{2} \sin{\left(x \right)}} + \frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{x^{2} \sin{\left(x \right)}}\right) + \frac{2^{2 x} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(2 \right)}^{4} \log{\left(x \right)}}{x \sin{\left(x \right)}} - \frac{2 \cdot 2^{x} \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(2 \right)}^{2} \log{\left(x \right)}}{x \sin{\left(x \right)}} + \frac{2^{x} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(2 \right)}^{3} \log{\left(x \right)}}{x \sin{\left(x \right)}} - \frac{2 \cdot 2^{x} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(2 \right)}^{2} \log{\left(x \right)} \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} - \frac{2 \cdot 2^{x} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(2 \right)}^{2} \log{\left(x \right)}}{x^{2} \sin{\left(x \right)}} + \frac{2 \cdot 2^{x} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(2 \right)}^{2}}{x^{2} \sin{\left(x \right)}} + \left(2^{3 x} \log{\left(2 \right)}^{6} \log{\left(x \right)} + 3 \cdot 2^{2 x} \log{\left(2 \right)}^{5} \log{\left(x \right)} + \frac{3 \cdot 2^{2 x} \log{\left(2 \right)}^{4}}{x} + 2^{x} \log{\left(2 \right)}^{4} \log{\left(x \right)} + \frac{3 \cdot 2^{x} \log{\left(2 \right)}^{3}}{x} - \frac{3 \cdot 2^{x} \log{\left(2 \right)}^{2}}{x^{2}} + \frac{2}{x^{3}}\right) \log{\left(x \sin{\left(x \right)} \right)} - \frac{\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \left(2^{x} \log{\left(2 \right)}^{2} \log{\left(x \right)} + \frac{1}{x}\right)}{x \sin{\left(x \right)}} + \frac{2 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x \right)} \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(2^{x} \log{\left(2 \right)}^{2} \log{\left(x \right)} + \frac{1}{x}\right) \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(2^{2 x} \log{\left(2 \right)}^{4} \log{\left(x \right)} + 2^{x} \log{\left(2 \right)}^{3} \log{\left(x \right)} + \frac{2 \cdot 2^{x} \log{\left(2 \right)}^{2}}{x} - \frac{1}{x^{2}}\right)}{x \sin{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{x \sin{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)} \cos^{2}{\left(x \right)}}{x \sin^{3}{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + 3 \sin{\left(x \right)}\right) \log{\left(x \right)}}{x \sin{\left(x \right)}} + \frac{2 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x \right)}}{x^{2} \sin{\left(x \right)}} - \frac{2 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right)}{x^{2} \sin{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(2^{x} \log{\left(2 \right)}^{2} \log{\left(x \right)} + \frac{1}{x}\right)}{x^{2} \sin{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)} \cos{\left(x \right)}}{x^{2} \sin^{2}{\left(x \right)}} - \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \right)}}{x^{2} \sin^{2}{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{x^{3} \sin{\left(x \right)}} - \frac{3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{x^{3} \sin{\left(x \right)}}\right)
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