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x^sin^4x
Derivada de la función/ x^sin/ sin^4/ x^sin^4x

Derivada de x^sin^4x

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
    4   
 sin (x)
x
xsin⁡4(x)x^{\sin^{4}{\left(x \right)}} 
x^(sin(x)^4)
Solución detallada

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

    Perola derivada

    (log⁡(sin⁡4(x))+1)∣sin⁡(x)∣4sin⁡4(x)\left(\log{\left(\sin^{4}{\left(x \right)} \right)} + 1\right) \left|{\sin{\left(x \right)}}\right|^{4 \sin^{4}{\left(x \right)}}

Respuesta:

(log⁡(sin⁡4(x))+1)∣sin⁡(x)∣4sin⁡4(x)\left(\log{\left(\sin^{4}{\left(x \right)} \right)} + 1\right) \left|{\sin{\left(x \right)}}\right|^{4 \sin^{4}{\left(x \right)}}

Gráfica
02468-8-6-4-2-1010-2525
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    4    /   4                             \
 sin (x) |sin (x)        3                 |
x       *|------- + 4*sin (x)*cos(x)*log(x)|
         \   x                             /
xsin⁡4(x)(4log⁡(x)sin⁡3(x)cos⁡(x)+sin⁡4(x)x)x^{\sin^{4}{\left(x \right)}} \left(4 \log{\left(x \right)} \sin^{3}{\left(x \right)} \cos{\left(x \right)} + \frac{\sin^{4}{\left(x \right)}}{x}\right)
Simplificar
Segunda derivada [src] 
    4            /                          2              2                                                            \
 sin (x)    2    |/sin(x)                  \     4      sin (x)        2                   2             8*cos(x)*sin(x)|
x       *sin (x)*||------ + 4*cos(x)*log(x)| *sin (x) - ------- - 4*sin (x)*log(x) + 12*cos (x)*log(x) + ---------------|
                 |\  x                     /                2                                                   x       |
                 \                                         x                                                            /
xsin⁡4(x)((4log⁡(x)cos⁡(x)+sin⁡(x)x)2sin⁡4(x)−4log⁡(x)sin⁡2(x)+12log⁡(x)cos⁡2(x)+8sin⁡(x)cos⁡(x)x−sin⁡2(x)x2)sin⁡2(x)x^{\sin^{4}{\left(x \right)}} \left(\left(4 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} \sin^{4}{\left(x \right)} - 4 \log{\left(x \right)} \sin^{2}{\left(x \right)} + 12 \log{\left(x \right)} \cos^{2}{\left(x \right)} + \frac{8 \sin{\left(x \right)} \cos{\left(x \right)}}{x} - \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right) \sin^{2}{\left(x \right)}
Simplificar
Tercera derivada [src] 
    4    /                          3                 3           3                                                           2                                                  /   2                                                            \         2          \       
 sin (x) |/sin(x)                  \     8      12*sin (x)   2*sin (x)         3                   2                    12*sin (x)*cos(x)        4    /sin(x)                  \ |sin (x)         2                  2             8*cos(x)*sin(x)|   36*cos (x)*sin(x)|       
x       *||------ + 4*cos(x)*log(x)| *sin (x) - ---------- + --------- + 24*cos (x)*log(x) - 40*sin (x)*cos(x)*log(x) - ----------------- - 3*sin (x)*|------ + 4*cos(x)*log(x)|*|------- - 12*cos (x)*log(x) + 4*sin (x)*log(x) - ---------------| + -----------------|*sin(x)
         |\  x                     /                x             3                                                              2                    \  x                     / |    2                                                   x       |           x        |       
         \                                                       x                                                              x                                                \   x                                                            /                    /
xsin⁡4(x)((4log⁡(x)cos⁡(x)+sin⁡(x)x)3sin⁡8(x)−3(4log⁡(x)cos⁡(x)+sin⁡(x)x)(4log⁡(x)sin⁡2(x)−12log⁡(x)cos⁡2(x)−8sin⁡(x)cos⁡(x)x+sin⁡2(x)x2)sin⁡4(x)−40log⁡(x)sin⁡2(x)cos⁡(x)+24log⁡(x)cos⁡3(x)−12sin⁡3(x)x+36sin⁡(x)cos⁡2(x)x−12sin⁡2(x)cos⁡(x)x2+2sin⁡3(x)x3)sin⁡(x)x^{\sin^{4}{\left(x \right)}} \left(\left(4 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{3} \sin^{8}{\left(x \right)} - 3 \left(4 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(4 \log{\left(x \right)} \sin^{2}{\left(x \right)} - 12 \log{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{8 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right) \sin^{4}{\left(x \right)} - 40 \log{\left(x \right)} \sin^{2}{\left(x \right)} \cos{\left(x \right)} + 24 \log{\left(x \right)} \cos^{3}{\left(x \right)} - \frac{12 \sin^{3}{\left(x \right)}}{x} + \frac{36 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{x} - \frac{12 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{x^{2}} + \frac{2 \sin^{3}{\left(x \right)}}{x^{3}}\right) \sin{\left(x \right)}
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Gráfico
Derivada de x^sin^4x
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