Sr Examen

Otras calculadoras

y=√x^(sin2x)
Derivada de la función/ sin2x/ y=√x^(sin2x)

Derivada de y=√x^(sin2x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

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

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

    Perola derivada

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

Respuesta:

(log⁡(sin⁡(2x))+1)sin⁡sin⁡(2x)(2x)\left(\log{\left(\sin{\left(2 x \right)} \right)} + 1\right) \sin^{\sin{\left(2 x \right)}}{\left(2 x \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        *|-------- + 2*cos(2*x)*log\\/ x /|
          \  2*x                           /
xsin⁡(2x)2(2log⁡(x)cos⁡(2x)+sin⁡(2x)2x)x^{\frac{\sin{\left(2 x \right)}}{2}} \left(2 \log{\left(\sqrt{x} \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{2 x}\right)
Simplificar
Segunda derivada [src] 
 sin(2*x) /                                                  /sin(2*x)                    \ /sin(2*x)                 /  ___\\\
 -------- |                                                  |-------- + 2*cos(2*x)*log(x)|*|-------- + 4*cos(2*x)*log\\/ x /||
    2     |       /  ___\            2*cos(2*x)   sin(2*x)   \   x                        / \   x                            /|
x        *|- 4*log\\/ x /*sin(2*x) + ---------- - -------- + -----------------------------------------------------------------|
          |                              x             2                                     4                                |
          \                                         2*x                                                                       /
xsin⁡(2x)2((4log⁡(x)cos⁡(2x)+sin⁡(2x)x)(2log⁡(x)cos⁡(2x)+sin⁡(2x)x)4−4log⁡(x)sin⁡(2x)+2cos⁡(2x)x−sin⁡(2x)2x2)x^{\frac{\sin{\left(2 x \right)}}{2}} \left(\frac{\left(4 \log{\left(\sqrt{x} \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x}\right) \left(2 \log{\left(x \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x}\right)}{4} - 4 \log{\left(\sqrt{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] 
          /                                                             /sin(2*x)                    \ /sin(2*x)   4*cos(2*x)        /  ___\         \   /sin(2*x)                 /  ___\\ /sin(2*x)   4*cos(2*x)                    \                                 2                                   \
 sin(2*x) |                                                             |-------- + 2*cos(2*x)*log(x)|*|-------- - ---------- + 8*log\\/ x /*sin(2*x)|   |-------- + 4*cos(2*x)*log\\/ x /|*|-------- - ---------- + 4*log(x)*sin(2*x)|   /sin(2*x)                    \  /sin(2*x)                 /  ___\\|
 -------- |                                                             \   x                        / |    2          x                             |   \   x                            / |    2          x                         |   |-------- + 2*cos(2*x)*log(x)| *|-------- + 4*cos(2*x)*log\\/ x /||
    2     |sin(2*x)                 /  ___\   6*sin(2*x)   3*cos(2*x)                                  \   x                                         /                                      \   x                                     /   \   x                        /  \   x                            /|
x        *|-------- - 8*cos(2*x)*log\\/ x / - ---------- - ---------- - ------------------------------------------------------------------------------ - ------------------------------------------------------------------------------ + ------------------------------------------------------------------|
          |    3                                  x             2                                             2                                                                                4                                                                          8                                 |
          \   x                                                x                                                                                                                                                                                                                                            /
xsin⁡(2x)2((4log⁡(x)cos⁡(2x)+sin⁡(2x)x)(2log⁡(x)cos⁡(2x)+sin⁡(2x)x)28−(4log⁡(x)cos⁡(2x)+sin⁡(2x)x)(4log⁡(x)sin⁡(2x)−4cos⁡(2x)x+sin⁡(2x)x2)4−(2log⁡(x)cos⁡(2x)+sin⁡(2x)x)(8log⁡(x)sin⁡(2x)−4cos⁡(2x)x+sin⁡(2x)x2)2−8log⁡(x)cos⁡(2x)−6sin⁡(2x)x−3cos⁡(2x)x2+sin⁡(2x)x3)x^{\frac{\sin{\left(2 x \right)}}{2}} \left(\frac{\left(4 \log{\left(\sqrt{x} \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x}\right) \left(2 \log{\left(x \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x}\right)^{2}}{8} - \frac{\left(4 \log{\left(\sqrt{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} - \frac{\left(2 \log{\left(x \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x}\right) \left(8 \log{\left(\sqrt{x} \right)} \sin{\left(2 x \right)} - \frac{4 \cos{\left(2 x \right)}}{x} + \frac{\sin{\left(2 x \right)}}{x^{2}}\right)}{2} - 8 \log{\left(\sqrt{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)
Simplificar
Gráfico
Derivada de y=√x^(sin2x)
    © Sr Examen – Калькулятор