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x^ln(cos(x))
Derivada de la función/ cos(x)/ x^ln(cos(x))

Derivada de x^ln(cos(x))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
 log(cos(x))
x
xlog⁡(cos⁡(x))x^{\log{\left(\cos{\left(x \right)} \right)}} 
x^log(cos(x))
Solución detallada

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

    Perola derivada

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

Respuesta:

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

Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
 log(cos(x)) /log(cos(x))   log(x)*sin(x)\
x           *|----------- - -------------|
             \     x            cos(x)   /
xlog⁡(cos⁡(x))(−log⁡(x)sin⁡(x)cos⁡(x)+log⁡(cos⁡(x))x)x^{\log{\left(\cos{\left(x \right)} \right)}} \left(- \frac{\log{\left(x \right)} \sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\log{\left(\cos{\left(x \right)} \right)}}{x}\right)
Simplificar
Segunda derivada [src] 
             /                               2                             2                     \
 log(cos(x)) |/  log(cos(x))   log(x)*sin(x)\             log(cos(x))   sin (x)*log(x)   2*sin(x)|
x           *||- ----------- + -------------|  - log(x) - ----------- - -------------- - --------|
             |\       x            cos(x)   /                   2             2          x*cos(x)|
             \                                                 x           cos (x)               /
xlog⁡(cos⁡(x))((log⁡(x)sin⁡(x)cos⁡(x)−log⁡(cos⁡(x))x)2−log⁡(x)sin⁡2(x)cos⁡2(x)−log⁡(x)−2sin⁡(x)xcos⁡(x)−log⁡(cos⁡(x))x2)x^{\log{\left(\cos{\left(x \right)} \right)}} \left(\left(\frac{\log{\left(x \right)} \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{\log{\left(\cos{\left(x \right)} \right)}}{x}\right)^{2} - \frac{\log{\left(x \right)} \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} - \log{\left(x \right)} - \frac{2 \sin{\left(x \right)}}{x \cos{\left(x \right)}} - \frac{\log{\left(\cos{\left(x \right)} \right)}}{x^{2}}\right)
Simplificar
Tercera derivada [src] 
             /                                 3                                                         /                 2                              \        2                             3                      \
 log(cos(x)) |  /  log(cos(x))   log(x)*sin(x)\    3   2*log(cos(x))     /  log(cos(x))   log(x)*sin(x)\ |log(cos(x))   sin (x)*log(x)   2*sin(x)         |   3*sin (x)   2*log(x)*sin(x)   2*sin (x)*log(x)    3*sin(x)|
x           *|- |- ----------- + -------------|  - - + ------------- + 3*|- ----------- + -------------|*|----------- + -------------- + -------- + log(x)| - --------- - --------------- - ---------------- + ---------|
             |  \       x            cos(x)   /    x          3          \       x            cos(x)   / |      2             2          x*cos(x)         |        2           cos(x)              3            2       |
             \                                               x                                           \     x           cos (x)                        /   x*cos (x)                         cos (x)        x *cos(x)/
xlog⁡(cos⁡(x))(−(log⁡(x)sin⁡(x)cos⁡(x)−log⁡(cos⁡(x))x)3+3(log⁡(x)sin⁡(x)cos⁡(x)−log⁡(cos⁡(x))x)(log⁡(x)sin⁡2(x)cos⁡2(x)+log⁡(x)+2sin⁡(x)xcos⁡(x)+log⁡(cos⁡(x))x2)−2log⁡(x)sin⁡3(x)cos⁡3(x)−2log⁡(x)sin⁡(x)cos⁡(x)−3sin⁡2(x)xcos⁡2(x)−3x+3sin⁡(x)x2cos⁡(x)+2log⁡(cos⁡(x))x3)x^{\log{\left(\cos{\left(x \right)} \right)}} \left(- \left(\frac{\log{\left(x \right)} \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{\log{\left(\cos{\left(x \right)} \right)}}{x}\right)^{3} + 3 \left(\frac{\log{\left(x \right)} \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{\log{\left(\cos{\left(x \right)} \right)}}{x}\right) \left(\frac{\log{\left(x \right)} \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \log{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x \cos{\left(x \right)}} + \frac{\log{\left(\cos{\left(x \right)} \right)}}{x^{2}}\right) - \frac{2 \log{\left(x \right)} \sin^{3}{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{2 \log{\left(x \right)} \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{3 \sin^{2}{\left(x \right)}}{x \cos^{2}{\left(x \right)}} - \frac{3}{x} + \frac{3 \sin{\left(x \right)}}{x^{2} \cos{\left(x \right)}} + \frac{2 \log{\left(\cos{\left(x \right)} \right)}}{x^{3}}\right)
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Gráfico
Derivada de x^ln(cos(x))
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