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x^x^sinx^3
Derivada de la función/ x^sin/ sinx^3/ x^x^sinx^3

Derivada de x^x^sinx^3

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

Gráfico:

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Solución

Ha introducido [src] 
 /    3   \
 | sin (x)|
 \x       /
x
xxsin⁡3(x)x^{x^{\sin^{3}{\left(x \right)}}} 
x^(x^(sin(x)^3))
Solución detallada

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

    Perola derivada

    (log⁡(xsin⁡3(x))+1)(xsin⁡3(x))xsin⁡3(x)\left(\log{\left(x^{\sin^{3}{\left(x \right)}} \right)} + 1\right) \left(x^{\sin^{3}{\left(x \right)}}\right)^{x^{\sin^{3}{\left(x \right)}}}

Respuesta:

(log⁡(xsin⁡3(x))+1)(xsin⁡3(x))xsin⁡3(x)\left(\log{\left(x^{\sin^{3}{\left(x \right)}} \right)} + 1\right) \left(x^{\sin^{3}{\left(x \right)}}\right)^{x^{\sin^{3}{\left(x \right)}}}

Gráfica
02468-8-6-4-2-1010-100000000100000000
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Primera derivada [src] 
 /    3   \ /    3                                                         \
 | sin (x)| | sin (x)       3    /   3                             \       |
 \x       / |x           sin (x) |sin (x)        2                 |       |
x          *|-------- + x       *|------- + 3*sin (x)*cos(x)*log(x)|*log(x)|
            \   x                \   x                             /       /
xxsin⁡3(x)(xsin⁡3(x)(3log⁡(x)sin⁡2(x)cos⁡(x)+sin⁡3(x)x)log⁡(x)+xsin⁡3(x)x)x^{x^{\sin^{3}{\left(x \right)}}} \left(x^{\sin^{3}{\left(x \right)}} \left(3 \log{\left(x \right)} \sin^{2}{\left(x \right)} \cos{\left(x \right)} + \frac{\sin^{3}{\left(x \right)}}{x}\right) \log{\left(x \right)} + \frac{x^{\sin^{3}{\left(x \right)}}}{x}\right)
Simplificar
Segunda derivada [src] 
 /    3   \          /                                                                                                                                                                                                       2    /sin(x)                  \\
 | sin (x)|     3    |           3                                                   2                             2                  /   2                                                           \                 2*sin (x)*|------ + 3*cos(x)*log(x)||
 \x       /  sin (x) |  1     sin (x) /1      2    /sin(x)                  \       \    /sin(x)                  \     4             |sin (x)        2                  2             6*cos(x)*sin(x)|                           \  x                     /|
x          *x       *|- -- + x       *|- + sin (x)*|------ + 3*cos(x)*log(x)|*log(x)|  + |------ + 3*cos(x)*log(x)| *sin (x)*log(x) - |------- - 6*cos (x)*log(x) + 3*sin (x)*log(x) - ---------------|*log(x)*sin(x) + ------------------------------------|
                     |   2            \x           \  x                     /       /    \  x                     /                   |    2                                                  x       |                                  x                  |
                     \  x                                                                                                             \   x                                                           /                                                     /
xxsin⁡3(x)xsin⁡3(x)(xsin⁡3(x)((3log⁡(x)cos⁡(x)+sin⁡(x)x)log⁡(x)sin⁡2(x)+1x)2+(3log⁡(x)cos⁡(x)+sin⁡(x)x)2log⁡(x)sin⁡4(x)−(3log⁡(x)sin⁡2(x)−6log⁡(x)cos⁡2(x)−6sin⁡(x)cos⁡(x)x+sin⁡2(x)x2)log⁡(x)sin⁡(x)+2(3log⁡(x)cos⁡(x)+sin⁡(x)x)sin⁡2(x)x−1x2)x^{x^{\sin^{3}{\left(x \right)}}} x^{\sin^{3}{\left(x \right)}} \left(x^{\sin^{3}{\left(x \right)}} \left(\left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(x \right)} \sin^{2}{\left(x \right)} + \frac{1}{x}\right)^{2} + \left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} \log{\left(x \right)} \sin^{4}{\left(x \right)} - \left(3 \log{\left(x \right)} \sin^{2}{\left(x \right)} - 6 \log{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{6 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)} \sin{\left(x \right)} + \frac{2 \left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \sin^{2}{\left(x \right)}}{x} - \frac{1}{x^{2}}\right)
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Tercera derivada [src] 
                     /                                                                                                                                                                                                                                          /   2                                                           \                                                                                                                                                                                                                                                                                                                                                                                                                                                \
                     |                                                                                                                                                                                                                                          |sin (x)        2                  2             6*cos(x)*sin(x)|                                                                             2                                                                                                                                                                                                                                                                                                                                                                  |
 /    3   \          |                                                                                                                                                                                                                                        3*|------- - 6*cos (x)*log(x) + 3*sin (x)*log(x) - ---------------|*sin(x)        2    /sin(x)                  \     /sin(x)                  \     4                                                                 /                                                                                                                                           2    /sin(x)                  \\                                                                                                                |
 | sin (x)|     3    |           3                                                   3   /                          3           3            2                  2                                     \                                    3                    |    2                                                  x       |          3*sin (x)*|------ + 3*cos(x)*log(x)|   3*|------ + 3*cos(x)*log(x)| *sin (x)         3                                                    |                                 2                  /   2                                                           \                 2*sin (x)*|------ + 3*cos(x)*log(x)||                                        /   2                                                           \       |
 \x       /  sin (x) |2     2*sin (x) /1      2    /sin(x)                  \       \    |       3             2*sin (x)   9*sin (x)   18*cos (x)*sin(x)   9*sin (x)*cos(x)         2                 |          /sin(x)                  \     6               \   x                                                           /                    \  x                     /     \  x                     /               sin (x) /1      2    /sin(x)                  \       \ |  1    /sin(x)                  \     4             |sin (x)        2                  2             6*cos(x)*sin(x)|                           \  x                     /|        3    /sin(x)                  \ |sin (x)        2                  2             6*cos(x)*sin(x)|       |
x          *x       *|-- + x         *|- + sin (x)*|------ + 3*cos(x)*log(x)|*log(x)|  - |- 6*cos (x)*log(x) - --------- + --------- - ----------------- + ---------------- + 21*sin (x)*cos(x)*log(x)|*log(x) + |------ + 3*cos(x)*log(x)| *sin (x)*log(x) - -------------------------------------------------------------------------- - ------------------------------------ + ------------------------------------- + 3*x       *|- + sin (x)*|------ + 3*cos(x)*log(x)|*log(x)|*|- -- + |------ + 3*cos(x)*log(x)| *sin (x)*log(x) - |------- - 6*cos (x)*log(x) + 3*sin (x)*log(x) - ---------------|*log(x)*sin(x) + ------------------------------------| - 3*sin (x)*|------ + 3*cos(x)*log(x)|*|------- - 6*cos (x)*log(x) + 3*sin (x)*log(x) - ---------------|*log(x)|
                     | 3              \x           \  x                     /       /    |                          3          x               x                   2                                  |          \  x                     /                                                       x                                                          2                                      x                                \x           \  x                     /       / |   2   \  x                     /                   |    2                                                  x       |                                  x                  |             \  x                     / |    2                                                  x       |       |
                     \x                                                                  \                         x                                              x                                   /                                                                                                                                                     x                                                                                                                        \  x                                                 \   x                                                           /                                                     /                                        \   x                                                           /       /
xxsin⁡3(x)xsin⁡3(x)(x2sin⁡3(x)((3log⁡(x)cos⁡(x)+sin⁡(x)x)log⁡(x)sin⁡2(x)+1x)3+3xsin⁡3(x)((3log⁡(x)cos⁡(x)+sin⁡(x)x)log⁡(x)sin⁡2(x)+1x)((3log⁡(x)cos⁡(x)+sin⁡(x)x)2log⁡(x)sin⁡4(x)−(3log⁡(x)sin⁡2(x)−6log⁡(x)cos⁡2(x)−6sin⁡(x)cos⁡(x)x+sin⁡2(x)x2)log⁡(x)sin⁡(x)+2(3log⁡(x)cos⁡(x)+sin⁡(x)x)sin⁡2(x)x−1x2)+(3log⁡(x)cos⁡(x)+sin⁡(x)x)3log⁡(x)sin⁡6(x)−3(3log⁡(x)cos⁡(x)+sin⁡(x)x)(3log⁡(x)sin⁡2(x)−6log⁡(x)cos⁡2(x)−6sin⁡(x)cos⁡(x)x+sin⁡2(x)x2)log⁡(x)sin⁡3(x)−(21log⁡(x)sin⁡2(x)cos⁡(x)−6log⁡(x)cos⁡3(x)+9sin⁡3(x)x−18sin⁡(x)cos⁡2(x)x+9sin⁡2(x)cos⁡(x)x2−2sin⁡3(x)x3)log⁡(x)+3(3log⁡(x)cos⁡(x)+sin⁡(x)x)2sin⁡4(x)x−3(3log⁡(x)sin⁡2(x)−6log⁡(x)cos⁡2(x)−6sin⁡(x)cos⁡(x)x+sin⁡2(x)x2)sin⁡(x)x−3(3log⁡(x)cos⁡(x)+sin⁡(x)x)sin⁡2(x)x2+2x3)x^{x^{\sin^{3}{\left(x \right)}}} x^{\sin^{3}{\left(x \right)}} \left(x^{2 \sin^{3}{\left(x \right)}} \left(\left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(x \right)} \sin^{2}{\left(x \right)} + \frac{1}{x}\right)^{3} + 3 x^{\sin^{3}{\left(x \right)}} \left(\left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(x \right)} \sin^{2}{\left(x \right)} + \frac{1}{x}\right) \left(\left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} \log{\left(x \right)} \sin^{4}{\left(x \right)} - \left(3 \log{\left(x \right)} \sin^{2}{\left(x \right)} - 6 \log{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{6 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)} \sin{\left(x \right)} + \frac{2 \left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \sin^{2}{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) + \left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{3} \log{\left(x \right)} \sin^{6}{\left(x \right)} - 3 \left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(3 \log{\left(x \right)} \sin^{2}{\left(x \right)} - 6 \log{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{6 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)} \sin^{3}{\left(x \right)} - \left(21 \log{\left(x \right)} \sin^{2}{\left(x \right)} \cos{\left(x \right)} - 6 \log{\left(x \right)} \cos^{3}{\left(x \right)} + \frac{9 \sin^{3}{\left(x \right)}}{x} - \frac{18 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{x} + \frac{9 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{x^{2}} - \frac{2 \sin^{3}{\left(x \right)}}{x^{3}}\right) \log{\left(x \right)} + \frac{3 \left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} \sin^{4}{\left(x \right)}}{x} - \frac{3 \left(3 \log{\left(x \right)} \sin^{2}{\left(x \right)} - 6 \log{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{6 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right) \sin{\left(x \right)}}{x} - \frac{3 \left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \sin^{2}{\left(x \right)}}{x^{2}} + \frac{2}{x^{3}}\right)
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Gráfico
Derivada de x^x^sinx^3
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