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

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

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

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

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

    Perola derivada

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

Respuesta:

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

Gráfica
02468-8-6-4-2-1010-5050
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
        2    /   2                              \
     sin (x) |sin (x)                           |
(2*x)       *|------- + 2*cos(x)*log(2*x)*sin(x)|
             \   x                              /
(2x)sin⁡2(x)(2log⁡(2x)sin⁡(x)cos⁡(x)+sin⁡2(x)x)\left(2 x\right)^{\sin^{2}{\left(x \right)}} \left(2 \log{\left(2 x \right)} \sin{\left(x \right)} \cos{\left(x \right)} + \frac{\sin^{2}{\left(x \right)}}{x}\right)
Simplificar
Segunda derivada [src] 
        2    /                            2              2                                                               \
     sin (x) |/sin(x)                    \     2      sin (x)        2                    2               4*cos(x)*sin(x)|
(2*x)       *||------ + 2*cos(x)*log(2*x)| *sin (x) - ------- - 2*sin (x)*log(2*x) + 2*cos (x)*log(2*x) + ---------------|
             |\  x                       /                2                                                      x       |
             \                                           x                                                               /
(2x)sin⁡2(x)((2log⁡(2x)cos⁡(x)+sin⁡(x)x)2sin⁡2(x)−2log⁡(2x)sin⁡2(x)+2log⁡(2x)cos⁡2(x)+4sin⁡(x)cos⁡(x)x−sin⁡2(x)x2)\left(2 x\right)^{\sin^{2}{\left(x \right)}} \left(\left(2 \log{\left(2 x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} \sin^{2}{\left(x \right)} - 2 \log{\left(2 x \right)} \sin^{2}{\left(x \right)} + 2 \log{\left(2 x \right)} \cos^{2}{\left(x \right)} + \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{x} - \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right)
Simplificar
Tercera derivada [src] 
        2    /                            3                2           2           2                                                                                  /   2                                                               \       \
     sin (x) |/sin(x)                    \     3      6*sin (x)   2*sin (x)   6*cos (x)                              6*cos(x)*sin(x)     /sin(x)                    \ |sin (x)        2                    2               4*cos(x)*sin(x)|       |
(2*x)       *||------ + 2*cos(x)*log(2*x)| *sin (x) - --------- + --------- + --------- - 8*cos(x)*log(2*x)*sin(x) - --------------- - 3*|------ + 2*cos(x)*log(2*x)|*|------- - 2*cos (x)*log(2*x) + 2*sin (x)*log(2*x) - ---------------|*sin(x)|
             |\  x                       /                x            3          x                                          2           \  x                       / |    2                                                      x       |       |
             \                                                        x                                                     x                                         \   x                                                               /       /
(2x)sin⁡2(x)((2log⁡(2x)cos⁡(x)+sin⁡(x)x)3sin⁡3(x)−3(2log⁡(2x)cos⁡(x)+sin⁡(x)x)(2log⁡(2x)sin⁡2(x)−2log⁡(2x)cos⁡2(x)−4sin⁡(x)cos⁡(x)x+sin⁡2(x)x2)sin⁡(x)−8log⁡(2x)sin⁡(x)cos⁡(x)−6sin⁡2(x)x+6cos⁡2(x)x−6sin⁡(x)cos⁡(x)x2+2sin⁡2(x)x3)\left(2 x\right)^{\sin^{2}{\left(x \right)}} \left(\left(2 \log{\left(2 x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{3} \sin^{3}{\left(x \right)} - 3 \left(2 \log{\left(2 x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(2 \log{\left(2 x \right)} \sin^{2}{\left(x \right)} - 2 \log{\left(2 x \right)} \cos^{2}{\left(x \right)} - \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right) \sin{\left(x \right)} - 8 \log{\left(2 x \right)} \sin{\left(x \right)} \cos{\left(x \right)} - \frac{6 \sin^{2}{\left(x \right)}}{x} + \frac{6 \cos^{2}{\left(x \right)}}{x} - \frac{6 \sin{\left(x \right)} \cos{\left(x \right)}}{x^{2}} + \frac{2 \sin^{2}{\left(x \right)}}{x^{3}}\right)
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Gráfico
Derivada de (2*x)^((sin(x))^2)
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