Derivada de (x/tgx)^e^cosx

Ha introducido [src]

        / cos(x)\
        \E      /
/  x   \         
|------|         
\tan(x)/

\left(\frac{x}{\tan{\left(x \right)}}\right)^{e^{\cos{\left(x \right)}}}

(x/tan(x))^(E^cos(x))

Solución detallada

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

Perola derivada

$\left(\log{\left(e^{\cos{\left(x \right)}} \right)} + 1\right) e^{e^{\cos{\left(x \right)}} \cos{\left(x \right)}}$
Simplificamos:

$\left(\cos{\left(x \right)} + 1\right) e^{e^{\cos{\left(x \right)}} \cos{\left(x \right)}}$

Respuesta:

$\left(\cos{\left(x \right)} + 1\right) e^{e^{\cos{\left(x \right)}} \cos{\left(x \right)}}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

                   /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   /                                                                      2\                                                                                                         \        
                   |                                           3                                                                                                   /               /       2   \\                                                                                                                                                                                                                               /                                                                                  /               /       2   \\                                                                         \                           /               /       2   \\                                                                   |                 /       2   \       /       2   \       /       2   \ |                         2 /               /       2   \\                                                |        
                   |/       /       2   \                     \                                                           /       /       2   \\     /       2   \ |      1      x*\1 + tan (x)/|     /       /       2   \\                                                        /       /       2   \\             /       /       2   \\     /       /       2   \\            /       /       2   \                     \ |       /       2   \                                                /       2   \ |      1      x*\1 + tan (x)/|     /       /       2   \\                        /       /       2   \\|             /       2   \ |      1      x*\1 + tan (x)/|                          /       /       2   \\     /       2   \ |        3      3*\1 + tan (x)/   5*x*\1 + tan (x)/   3*x*\1 + tan (x)/ |            /       2   \  |      1      x*\1 + tan (x)/|                   /       /       2   \\       |        
         / cos(x)\ ||     x*\1 + tan (x)/                     |                                                           |     x*\1 + tan (x)/|   4*\1 + tan (x)/*|x + ------ - ---------------|     |     x*\1 + tan (x)/|                                          /       2   \ |     x*\1 + tan (x)/|        2    |     x*\1 + tan (x)/|     |     x*\1 + tan (x)/|            |     x*\1 + tan (x)/                     | |     x*\1 + tan (x)/                                              2*\1 + tan (x)/*|x + ------ - ---------------|     |     x*\1 + tan (x)/|          /       2   \ |     x*\1 + tan (x)/||           6*\1 + tan (x)/*|x + ------ - ---------------|*sin(x)     /       2   \ |     x*\1 + tan (x)/|   2*\1 + tan (x)/*|2*x + ------ - --------------- - ----------------- + ------------------|*tan(x)   4*\1 + tan (x)/ *|x + ------ - ---------------|     /       2   \ |     x*\1 + tan (x)/|       |        
         \e      / ||-1 + ---------------                     |                                                         2*|-1 + ---------------|                   |    tan(x)          2       |   3*|-1 + ---------------|*cos(x)                                 2*\1 + tan (x)/*|-1 + ---------------|   3*sin (x)*|-1 + ---------------|   3*|-1 + ---------------|*sin(x)     |-1 + ---------------                     | |-1 + ---------------                                                              |    tan(x)          2       |   2*|-1 + ---------------|*sin(x)   \1 + tan (x)/*|-1 + ---------------||                           |    tan(x)          2       |          2*\1 + tan (x)/*|-1 + ---------------|                   |      tan(x)          3                  2                   4         |                           |    tan(x)          2       |   3*\1 + tan (x)/*|-1 + ---------------|*sin(x)|        
 /  x   \          ||          tan(x)          /  x   \       |   2*cos(x)      3       /  x   \      /  x   \            \          tan(x)    /                   \                 tan (x)    /     \          tan(x)    /                      /  x   \                          \          tan(x)    /             \          tan(x)    /     \          tan(x)    /            |          tan(x)          /  x   \       | |          tan(x)          2       /  x   \             /  x   \                   \                 tan (x)    /     \          tan(x)    /                        \          tan(x)    /|  cos(x)                   \                 tan (x)    /                          \          tan(x)    /                   \                   tan (x)            tan (x)             tan (x)      /                           \                 tan (x)    /                   \          tan(x)    /       |  cos(x)
-|------|         *||-------------------- + log|------|*sin(x)| *e         + sin (x)*log|------| - log|------|*sin(x) + ------------------------ - ---------------------------------------------- - ------------------------------- - 3*cos(x)*log|------|*sin(x) + -------------------------------------- + -------------------------------- + ------------------------------- + 3*|-------------------- + log|------|*sin(x)|*|-------------------- + sin (x)*log|------| - cos(x)*log|------| - ---------------------------------------------- + ------------------------------- - ------------------------------------|*e       - ----------------------------------------------------- - -------------------------------------- + ------------------------------------------------------------------------------------------------ + ----------------------------------------------- - ---------------------------------------------|*e      
 \tan(x)/          |\         x                \tan(x)/       /                         \tan(x)/      \tan(x)/                      3                                     2                                        x                              \tan(x)/                            x                                     x                                   2                   \         x                \tan(x)/       / |          2                       \tan(x)/             \tan(x)/                         x                                         x                                x*tan(x)              |                                     x                                            2                                                                        x                                                                       x*tan(x)                                         x*tan(x)                  |        
                   \                                                                                                               x                                     x                                                                                                                                                                                     x                                                                \         x                                                                                                                                                                               /                                                                                 x *tan(x)                                                                                                                                                                                                                    /

- \left(\frac{x}{\tan{\left(x \right)}}\right)^{e^{\cos{\left(x \right)}}} \left(\left(\log{\left(\frac{x}{\tan{\left(x \right)}} \right)} \sin{\left(x \right)} + \frac{\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1}{x}\right)^{3} e^{2 \cos{\left(x \right)}} + 3 \left(\log{\left(\frac{x}{\tan{\left(x \right)}} \right)} \sin{\left(x \right)} + \frac{\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1}{x}\right) \left(\log{\left(\frac{x}{\tan{\left(x \right)}} \right)} \sin^{2}{\left(x \right)} - \log{\left(\frac{x}{\tan{\left(x \right)}} \right)} \cos{\left(x \right)} - \frac{\left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{x \tan{\left(x \right)}} + \frac{2 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right) \sin{\left(x \right)}}{x} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(- \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + x + \frac{1}{\tan{\left(x \right)}}\right)}{x} + \frac{\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1}{x^{2}}\right) e^{\cos{\left(x \right)}} + \log{\left(\frac{x}{\tan{\left(x \right)}} \right)} \sin^{3}{\left(x \right)} - 3 \log{\left(\frac{x}{\tan{\left(x \right)}} \right)} \sin{\left(x \right)} \cos{\left(x \right)} - \log{\left(\frac{x}{\tan{\left(x \right)}} \right)} \sin{\left(x \right)} - \frac{3 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)}}{x \tan{\left(x \right)}} + \frac{2 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{x} + \frac{3 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right) \sin^{2}{\left(x \right)}}{x} - \frac{3 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right) \cos{\left(x \right)}}{x} + \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \left(- \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + x + \frac{1}{\tan{\left(x \right)}}\right)}{x \tan{\left(x \right)}} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \left(- \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + x + \frac{1}{\tan{\left(x \right)}}\right) \sin{\left(x \right)}}{x} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{3 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{4}{\left(x \right)}} - \frac{5 x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + 2 x - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{3}{\left(x \right)}} + \frac{3}{\tan{\left(x \right)}}\right) \tan{\left(x \right)}}{x} - \frac{2 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2} \tan{\left(x \right)}} + \frac{3 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right) \sin{\left(x \right)}}{x^{2}} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \left(- \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + x + \frac{1}{\tan{\left(x \right)}}\right)}{x^{2}} + \frac{2 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - 1\right)}{x^{3}}\right) e^{\cos{\left(x \right)}}

Simplificar

Gráfico

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Derivada de (x/tgx)^e^cosx

Gráfico:

Definida a trozos:

Solución