Sr Examen

Otras calculadoras

(xsinx)^(2/x)
Derivada de la función/ xsinx/ (2/x)/ (xsinx)^(2/x)

Derivada de (xsinx)^(2/x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

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

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

    Perola derivada

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

Respuesta:

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

Gráfica
02468-8-6-4-2-1010-5e425e42
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
          2                                            
          -                                            
          x /  2*log(x*sin(x))   2*(x*cos(x) + sin(x))\
(x*sin(x)) *|- --------------- + ---------------------|
            |          2                2             |
            \         x                x *sin(x)      /
(xsin⁡(x))2x(2(xcos⁡(x)+sin⁡(x))x2sin⁡(x)−2log⁡(xsin⁡(x))x2)\left(x \sin{\left(x \right)}\right)^{\frac{2}{x}} \left(\frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{x^{2} \sin{\left(x \right)}} - \frac{2 \log{\left(x \sin{\left(x \right)} \right)}}{x^{2}}\right)
Simplificar
Segunda derivada [src] 
              /                                                                                 2                                                     \
            2 |                                             /                 x*cos(x) + sin(x)\                                                      |
            - |                                           2*|-log(x*sin(x)) + -----------------|                                                      |
            x |  -2*cos(x) + x*sin(x)   2*log(x*sin(x))     \                       sin(x)     /    (x*cos(x) + sin(x))*cos(x)   3*(x*cos(x) + sin(x))|
2*(x*sin(x)) *|- -------------------- + --------------- + --------------------------------------- - -------------------------- - ---------------------|
              |         sin(x)                 x                              2                                 2                       x*sin(x)      |
              \                                                              x                               sin (x)                                  /
-------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                            2                                                                          
                                                                           x
2(xsin⁡(x))2x(−xsin⁡(x)−2cos⁡(x)sin⁡(x)−(xcos⁡(x)+sin⁡(x))cos⁡(x)sin⁡2(x)−3(xcos⁡(x)+sin⁡(x))xsin⁡(x)+2log⁡(xsin⁡(x))x+2(xcos⁡(x)+sin⁡(x)sin⁡(x)−log⁡(xsin⁡(x)))2x2)x2\frac{2 \left(x \sin{\left(x \right)}\right)^{\frac{2}{x}} \left(- \frac{x \sin{\left(x \right)} - 2 \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{x \sin{\left(x \right)}} + \frac{2 \log{\left(x \sin{\left(x \right)} \right)}}{x} + \frac{2 \left(\frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{\sin{\left(x \right)}} - \log{\left(x \sin{\left(x \right)} \right)}\right)^{2}}{x^{2}}\right)}{x^{2}}
Simplificar
Tercera derivada [src] 
              /                                                                                                  3     /                 x*cos(x) + sin(x)\ /-2*cos(x) + x*sin(x)   2*log(x*sin(x))   (x*cos(x) + sin(x))*cos(x)   3*(x*cos(x) + sin(x))\                                                                                                                                                     \
            2 |                                                              /                 x*cos(x) + sin(x)\    6*|-log(x*sin(x)) + -----------------|*|-------------------- - --------------- + -------------------------- + ---------------------|                                                                                                                                                     |
            - |                                                            4*|-log(x*sin(x)) + -----------------|      \                       sin(x)     / |       sin(x)                 x                      2                       x*sin(x)      |        2                                                                                                                                            |
            x |x*cos(x) + sin(x)   3*sin(x) + x*cos(x)   6*log(x*sin(x))     \                       sin(x)     /                                           \                                                  sin (x)                                  /   2*cos (x)*(x*cos(x) + sin(x))   2*(-2*cos(x) + x*sin(x))*cos(x)   5*(-2*cos(x) + x*sin(x))   11*(x*cos(x) + sin(x))   5*(x*cos(x) + sin(x))*cos(x)|
2*(x*sin(x)) *|----------------- - ------------------- - --------------- + --------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------ + ----------------------------- + ------------------------------- + ------------------------ + ---------------------- + ----------------------------|
              |      sin(x)               sin(x)                 2                             4                                                                                       2                                                                                  3                                2                          x*sin(x)                  2                               2             |
              \                                                 x                             x                                                                                       x                                                                                sin (x)                          sin (x)                                                x *sin(x)                   x*sin (x)          /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                        2                                                                                                                                                                                                      
                                                                                                                                                                                                       x
2(xsin⁡(x))2x(2(xsin⁡(x)−2cos⁡(x))cos⁡(x)sin⁡2(x)+xcos⁡(x)+sin⁡(x)sin⁡(x)+2(xcos⁡(x)+sin⁡(x))cos⁡2(x)sin⁡3(x)−xcos⁡(x)+3sin⁡(x)sin⁡(x)+5(xsin⁡(x)−2cos⁡(x))xsin⁡(x)+5(xcos⁡(x)+sin⁡(x))cos⁡(x)xsin⁡2(x)+11(xcos⁡(x)+sin⁡(x))x2sin⁡(x)−6(xcos⁡(x)+sin⁡(x)sin⁡(x)−log⁡(xsin⁡(x)))(xsin⁡(x)−2cos⁡(x)sin⁡(x)+(xcos⁡(x)+sin⁡(x))cos⁡(x)sin⁡2(x)+3(xcos⁡(x)+sin⁡(x))xsin⁡(x)−2log⁡(xsin⁡(x))x)x2−6log⁡(xsin⁡(x))x2+4(xcos⁡(x)+sin⁡(x)sin⁡(x)−log⁡(xsin⁡(x)))3x4)x2\frac{2 \left(x \sin{\left(x \right)}\right)^{\frac{2}{x}} \left(\frac{2 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \cos{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos^{2}{\left(x \right)}}{\sin^{3}{\left(x \right)}} - \frac{x \cos{\left(x \right)} + 3 \sin{\left(x \right)}}{\sin{\left(x \right)}} + \frac{5 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right)}{x \sin{\left(x \right)}} + \frac{5 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} + \frac{11 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{x^{2} \sin{\left(x \right)}} - \frac{6 \left(\frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{\sin{\left(x \right)}} - \log{\left(x \sin{\left(x \right)} \right)}\right) \left(\frac{x \sin{\left(x \right)} - 2 \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{x \sin{\left(x \right)}} - \frac{2 \log{\left(x \sin{\left(x \right)} \right)}}{x}\right)}{x^{2}} - \frac{6 \log{\left(x \sin{\left(x \right)} \right)}}{x^{2}} + \frac{4 \left(\frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{\sin{\left(x \right)}} - \log{\left(x \sin{\left(x \right)} \right)}\right)^{3}}{x^{4}}\right)}{x^{2}}
Simplificar
Gráfico
Derivada de (xsinx)^(2/x)
    © Sr Examen – Калькулятор