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x^(sin2x/2)
Derivada de la función/ sin2x/ x^(sin2x/2)

Derivada de x^(sin2x/2)

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

Gráfico:

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Definida a trozos:

Solución

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

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

    Perola derivada

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

  2. Simplificamos:

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

Respuesta:

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

Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
 sin(2*x)                             
 --------                             
    2     /                  sin(2*x)\
x        *|cos(2*x)*log(x) + --------|
          \                    2*x   /
xsin⁡(2x)2(log⁡(x)cos⁡(2x)+sin⁡(2x)2x)x^{\frac{\sin{\left(2 x \right)}}{2}} \left(\log{\left(x \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{2 x}\right)
Simplificar
Segunda derivada [src] 
          /                              2                                            \
 sin(2*x) |/sin(2*x)                    \                                             |
 -------- ||-------- + 2*cos(2*x)*log(x)|                                             |
    2     |\   x                        /                        2*cos(2*x)   sin(2*x)|
x        *|------------------------------- - 2*log(x)*sin(2*x) + ---------- - --------|
          |               4                                          x             2  |
          \                                                                     2*x   /
xsin⁡(2x)2((2log⁡(x)cos⁡(2x)+sin⁡(2x)x)24−2log⁡(x)sin⁡(2x)+2cos⁡(2x)x−sin⁡(2x)2x2)x^{\frac{\sin{\left(2 x \right)}}{2}} \left(\frac{\left(2 \log{\left(x \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x}\right)^{2}}{4} - 2 \log{\left(x \right)} \sin{\left(2 x \right)} + \frac{2 \cos{\left(2 x \right)}}{x} - \frac{\sin{\left(2 x \right)}}{2 x^{2}}\right)
Simplificar
Tercera derivada [src] 
          /                              3                                                              /sin(2*x)                    \ /sin(2*x)   4*cos(2*x)                    \\
 sin(2*x) |/sin(2*x)                    \                                                             3*|-------- + 2*cos(2*x)*log(x)|*|-------- - ---------- + 4*log(x)*sin(2*x)||
 -------- ||-------- + 2*cos(2*x)*log(x)|                                                               \   x                        / |    2          x                         ||
    2     |\   x                        /    sin(2*x)   6*sin(2*x)                       3*cos(2*x)                                    \   x                                     /|
x        *|------------------------------- + -------- - ---------- - 4*cos(2*x)*log(x) - ---------- - ----------------------------------------------------------------------------|
          |               8                      3          x                                 2                                            4                                      |
          \                                     x                                            x                                                                                    /
xsin⁡(2x)2((2log⁡(x)cos⁡(2x)+sin⁡(2x)x)38−3(2log⁡(x)cos⁡(2x)+sin⁡(2x)x)(4log⁡(x)sin⁡(2x)−4cos⁡(2x)x+sin⁡(2x)x2)4−4log⁡(x)cos⁡(2x)−6sin⁡(2x)x−3cos⁡(2x)x2+sin⁡(2x)x3)x^{\frac{\sin{\left(2 x \right)}}{2}} \left(\frac{\left(2 \log{\left(x \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x}\right)^{3}}{8} - \frac{3 \left(2 \log{\left(x \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x}\right) \left(4 \log{\left(x \right)} \sin{\left(2 x \right)} - \frac{4 \cos{\left(2 x \right)}}{x} + \frac{\sin{\left(2 x \right)}}{x^{2}}\right)}{4} - 4 \log{\left(x \right)} \cos{\left(2 x \right)} - \frac{6 \sin{\left(2 x \right)}}{x} - \frac{3 \cos{\left(2 x \right)}}{x^{2}} + \frac{\sin{\left(2 x \right)}}{x^{3}}\right)
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Gráfico
Derivada de x^(sin2x/2)
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