Derivada de y=x^e^cosx

Ha introducido [src]

 / cos(x)\
 \E      /
x

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

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]

 / cos(x)\ / cos(x)                        \
 \E      / |e          cos(x)              |
x         *|------- - e      *log(x)*sin(x)|
           \   x                           /

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

Simplificar

Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

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

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

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Gráfico

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Derivada de y=x^e^cosx

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