Derivada de x^x^sinx

Ha introducido [src]

 / sin(x)\
 \x      /
x

x^{x^{\sin{\left(x \right)}}}

x^(x^sin(x))

Solución detallada

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Perola derivada

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

Respuesta:

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

Gráfica

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Primera derivada [src]

 / sin(x)\ / sin(x)                                          \
 \x      / |x          sin(x) /sin(x)                \       |
x         *|------- + x      *|------ + cos(x)*log(x)|*log(x)|
           \   x              \  x                   /       /

x^{x^{\sin{\left(x \right)}}} \left(x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(x \right)} + \frac{x^{\sin{\left(x \right)}}}{x}\right)

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Segunda derivada [src]

                   /                                                                                                                                          /sin(x)                \\
 / sin(x)\         |                                                    2                           2                                                       2*|------ + cos(x)*log(x)||
 \x      /  sin(x) |  1     sin(x) /1   /sin(x)                \       \    /sin(x)                \           /sin(x)                   2*cos(x)\            \  x                   /|
x         *x      *|- -- + x      *|- + |------ + cos(x)*log(x)|*log(x)|  + |------ + cos(x)*log(x)| *log(x) - |------ + log(x)*sin(x) - --------|*log(x) + --------------------------|
                   |   2           \x   \  x                   /       /    \  x                   /           |   2                        x    |                      x             |
                   \  x                                                                                        \  x                              /                                    /

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

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Tercera derivada [src]

                   /                                                                                                                                                       /sin(x)                   2*cos(x)\                                                          2                                                                                                                                                                                                                                              \
                   |                                                                                                                                                     3*|------ + log(x)*sin(x) - --------|     /sin(x)                \     /sin(x)                \                                                                                                                            /                                                                                         /sin(x)                \\|
 / sin(x)\         |                                                    3                           3                                                                      |   2                        x    |   3*|------ + cos(x)*log(x)|   3*|------ + cos(x)*log(x)|                                                                                                                            |                               2                                                       2*|------ + cos(x)*log(x)|||
 \x      /  sin(x) |2     2*sin(x) /1   /sin(x)                \       \    /sin(x)                \           /                2*sin(x)   3*sin(x)   3*cos(x)\            \  x                              /     \  x                   /     \  x                   /      /sin(x)                \ /sin(x)                   2*cos(x)\             sin(x) /1   /sin(x)                \       \ |  1    /sin(x)                \           /sin(x)                   2*cos(x)\            \  x                   /||
x         *x      *|-- + x        *|- + |------ + cos(x)*log(x)|*log(x)|  + |------ + cos(x)*log(x)| *log(x) - |cos(x)*log(x) - -------- + -------- + --------|*log(x) - ------------------------------------- - -------------------------- + --------------------------- - 3*|------ + cos(x)*log(x)|*|------ + log(x)*sin(x) - --------|*log(x) + 3*x      *|- + |------ + cos(x)*log(x)|*log(x)|*|- -- + |------ + cos(x)*log(x)| *log(x) - |------ + log(x)*sin(x) - --------|*log(x) + --------------------------||
                   | 3             \x   \  x                   /       /    \  x                   /           |                    3         x           2   |                            x                                  2                            x                  \  x                   / |   2                        x    |                    \x   \  x                   /       / |   2   \  x                   /           |   2                        x    |                      x             ||
                   \x                                                                                          \                   x                     x    /                                                              x                                                                         \  x                              /                                                          \  x                                       \  x                              /                                    //

x^{x^{\sin{\left(x \right)}}} x^{\sin{\left(x \right)}} \left(x^{2 \sin{\left(x \right)}} \left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right)^{3} + 3 x^{\sin{\left(x \right)}} \left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right) \left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} \log{\left(x \right)} - \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)}{x} - \frac{1}{x^{2}}\right) + \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{3} \log{\left(x \right)} - 3 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)} - \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{3 \sin{\left(x \right)}}{x} + \frac{3 \cos{\left(x \right)}}{x^{2}} - \frac{2 \sin{\left(x \right)}}{x^{3}}\right) \log{\left(x \right)} + \frac{3 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2}}{x} - \frac{3 \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right)}{x} - \frac{3 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)}{x^{2}} + \frac{2}{x^{3}}\right)

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Gráfico

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Derivada de x^x^sinx

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