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x^((sinx)^cosx)
Derivada de la función/ (sinx)/ x^((sinx)^cosx)

Derivada de x^((sinx)^cosx)

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

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Solución detallada

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    Perola derivada

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

Respuesta:

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

Gráfica
02468-8-6-4-2-1010-2e522e52
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Primera derivada [src] 
    cos(x)    /   cos(x)                   /   2                        \       \
 sin      (x) |sin      (x)      cos(x)    |cos (x)                     |       |
x            *|------------ + sin      (x)*|------- - log(sin(x))*sin(x)|*log(x)|
              \     x                      \ sin(x)                     /       /
xsin⁡cos⁡(x)(x)((−log⁡(sin⁡(x))sin⁡(x)+cos⁡2(x)sin⁡(x))log⁡(x)sin⁡cos⁡(x)(x)+sin⁡cos⁡(x)(x)x)x^{\sin^{\cos{\left(x \right)}}{\left(x \right)}} \left(\left(- \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} + \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) \log{\left(x \right)} \sin^{\cos{\left(x \right)}}{\left(x \right)} + \frac{\sin^{\cos{\left(x \right)}}{\left(x \right)}}{x}\right)
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Segunda derivada [src] 
                           /                                                                                                                /                        2   \                                            \
                           |                                                    2                                              2            |                     cos (x)|                                            |
    cos(x)                 |       /      /                        2   \       \                 /                        2   \           2*|log(sin(x))*sin(x) - -------|   /       2                 \              |
 sin      (x)    cos(x)    |  1    |  1   |                     cos (x)|       |     cos(x)      |                     cos (x)|             \                      sin(x)/   |    cos (x)              |              |
x            *sin      (x)*|- -- + |- - + |log(sin(x))*sin(x) - -------|*log(x)| *sin      (x) + |log(sin(x))*sin(x) - -------| *log(x) - -------------------------------- - |3 + ------- + log(sin(x))|*cos(x)*log(x)|
                           |   2   \  x   \                      sin(x)/       /                 \                      sin(x)/                          x                   |       2                 |              |
                           \  x                                                                                                                                              \    sin (x)              /              /
xsin⁡cos⁡(x)(x)(((log⁡(sin⁡(x))sin⁡(x)−cos⁡2(x)sin⁡(x))log⁡(x)−1x)2sin⁡cos⁡(x)(x)+(log⁡(sin⁡(x))sin⁡(x)−cos⁡2(x)sin⁡(x))2log⁡(x)−(log⁡(sin⁡(x))+3+cos⁡2(x)sin⁡2(x))log⁡(x)cos⁡(x)−2(log⁡(sin⁡(x))sin⁡(x)−cos⁡2(x)sin⁡(x))x−1x2)sin⁡cos⁡(x)(x)x^{\sin^{\cos{\left(x \right)}}{\left(x \right)}} \left(\left(\left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) \log{\left(x \right)} - \frac{1}{x}\right)^{2} \sin^{\cos{\left(x \right)}}{\left(x \right)} + \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} \log{\left(x \right)} - \left(\log{\left(\sin{\left(x \right)} \right)} + 3 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \log{\left(x \right)} \cos{\left(x \right)} - \frac{2 \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)}{x} - \frac{1}{x^{2}}\right) \sin^{\cos{\left(x \right)}}{\left(x \right)}
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Tercera derivada [src] 
                           /                                                                                                                                                                                                               2                                        /       2                 \                                                                                                                                                                                                                                                                                \
                           |                                                                                                                                                                                 /                        2   \      /                        2   \     |    cos (x)              |                                                                       /                                                /                        2   \                                            \                                                                             |
                           |                                                                                                                   3                                                3            |                     cos (x)|      |                     cos (x)|   3*|3 + ------- + log(sin(x))|*cos(x)                                                                |                                   2            |                     cos (x)|                                            |                                                                             |
    cos(x)                 |     /                                     2           4   \          /      /                        2   \       \                   /                        2   \           3*|log(sin(x))*sin(x) - -------|    3*|log(sin(x))*sin(x) - -------|     |       2                 |                         /      /                        2   \       \ |     /                        2   \           2*|log(sin(x))*sin(x) - -------|   /       2                 \              |     /                        2   \ /       2                 \              |
 sin      (x)    cos(x)    |2    |                                2*cos (x)   2*cos (x)|          |  1   |                     cos (x)|       |     2*cos(x)      |                     cos (x)|             \                      sin(x)/      \                      sin(x)/     \    sin (x)              /               cos(x)    |  1   |                     cos (x)|       | |1    |                     cos (x)|             \                      sin(x)/   |    cos (x)              |              |     |                     cos (x)| |    cos (x)              |              |
x            *sin      (x)*|-- + |3*sin(x) + log(sin(x))*sin(x) + --------- + ---------|*log(x) - |- - + |log(sin(x))*sin(x) - -------|*log(x)| *sin        (x) - |log(sin(x))*sin(x) - -------| *log(x) + --------------------------------- + -------------------------------- - ------------------------------------ + 3*sin      (x)*|- - + |log(sin(x))*sin(x) - -------|*log(x)|*|-- - |log(sin(x))*sin(x) - -------| *log(x) + -------------------------------- + |3 + ------- + log(sin(x))|*cos(x)*log(x)| + 3*|log(sin(x))*sin(x) - -------|*|3 + ------- + log(sin(x))|*cos(x)*log(x)|
                           | 3   |                                  sin(x)        3    |          \  x   \                      sin(x)/       /                   \                      sin(x)/                           x                                   2                                   x                                    \  x   \                      sin(x)/       / | 2   \                      sin(x)/                          x                   |       2                 |              |     \                      sin(x)/ |       2                 |              |
                           \x    \                                             sin (x) /                                                                                                                                                                      x                                                                                                                       \x                                                                                \    sin (x)              /              /                                    \    sin (x)              /              /
xsin⁡cos⁡(x)(x)(−((log⁡(sin⁡(x))sin⁡(x)−cos⁡2(x)sin⁡(x))log⁡(x)−1x)3sin⁡2cos⁡(x)(x)+3((log⁡(sin⁡(x))sin⁡(x)−cos⁡2(x)sin⁡(x))log⁡(x)−1x)(−(log⁡(sin⁡(x))sin⁡(x)−cos⁡2(x)sin⁡(x))2log⁡(x)+(log⁡(sin⁡(x))+3+cos⁡2(x)sin⁡2(x))log⁡(x)cos⁡(x)+2(log⁡(sin⁡(x))sin⁡(x)−cos⁡2(x)sin⁡(x))x+1x2)sin⁡cos⁡(x)(x)−(log⁡(sin⁡(x))sin⁡(x)−cos⁡2(x)sin⁡(x))3log⁡(x)+3(log⁡(sin⁡(x))sin⁡(x)−cos⁡2(x)sin⁡(x))(log⁡(sin⁡(x))+3+cos⁡2(x)sin⁡2(x))log⁡(x)cos⁡(x)+(log⁡(sin⁡(x))sin⁡(x)+3sin⁡(x)+2cos⁡2(x)sin⁡(x)+2cos⁡4(x)sin⁡3(x))log⁡(x)+3(log⁡(sin⁡(x))sin⁡(x)−cos⁡2(x)sin⁡(x))2x−3(log⁡(sin⁡(x))+3+cos⁡2(x)sin⁡2(x))cos⁡(x)x+3(log⁡(sin⁡(x))sin⁡(x)−cos⁡2(x)sin⁡(x))x2+2x3)sin⁡cos⁡(x)(x)x^{\sin^{\cos{\left(x \right)}}{\left(x \right)}} \left(- \left(\left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) \log{\left(x \right)} - \frac{1}{x}\right)^{3} \sin^{2 \cos{\left(x \right)}}{\left(x \right)} + 3 \left(\left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) \log{\left(x \right)} - \frac{1}{x}\right) \left(- \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} \log{\left(x \right)} + \left(\log{\left(\sin{\left(x \right)} \right)} + 3 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \log{\left(x \right)} \cos{\left(x \right)} + \frac{2 \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)}{x} + \frac{1}{x^{2}}\right) \sin^{\cos{\left(x \right)}}{\left(x \right)} - \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)^{3} \log{\left(x \right)} + 3 \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(\log{\left(\sin{\left(x \right)} \right)} + 3 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \log{\left(x \right)} \cos{\left(x \right)} + \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} + 3 \sin{\left(x \right)} + \frac{2 \cos^{2}{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \cos^{4}{\left(x \right)}}{\sin^{3}{\left(x \right)}}\right) \log{\left(x \right)} + \frac{3 \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2}}{x} - \frac{3 \left(\log{\left(\sin{\left(x \right)} \right)} + 3 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \cos{\left(x \right)}}{x} + \frac{3 \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)}{x^{2}} + \frac{2}{x^{3}}\right) \sin^{\cos{\left(x \right)}}{\left(x \right)}
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Gráfico
Derivada de x^((sinx)^cosx)
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