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x^cosx
Derivada de la función/ x^cosx

Derivada de x^cosx

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

Gráfico:

interior superior

Definida a trozos:

Solución

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

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

    Perola derivada

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

Respuesta:

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

Gráfica
02468-8-6-4-2-1010-1010
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
 cos(x) /cos(x)                \
x      *|------ - log(x)*sin(x)|
        \  x                   /
xcos⁡(x)(−log⁡(x)sin⁡(x)+cos⁡(x)x)x^{\cos{\left(x \right)}} \left(- \log{\left(x \right)} \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right)
Simplificar
Segunda derivada [src] 
        /                        2                                    \
 cos(x) |/                cos(x)\    cos(x)                   2*sin(x)|
x      *||log(x)*sin(x) - ------|  - ------ - cos(x)*log(x) - --------|
        |\                  x   /       2                        x    |
        \                              x                              /
xcos⁡(x)((log⁡(x)sin⁡(x)−cos⁡(x)x)2−log⁡(x)cos⁡(x)−2sin⁡(x)x−cos⁡(x)x2)x^{\cos{\left(x \right)}} \left(\left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right)^{2} - \log{\left(x \right)} \cos{\left(x \right)} - \frac{2 \sin{\left(x \right)}}{x} - \frac{\cos{\left(x \right)}}{x^{2}}\right)
Simplificar
Tercera derivada [src] 
        /                          3                                                                                                                  \
 cos(x) |  /                cos(x)\                    3*cos(x)   2*cos(x)   3*sin(x)     /                cos(x)\ /cos(x)                   2*sin(x)\|
x      *|- |log(x)*sin(x) - ------|  + log(x)*sin(x) - -------- + -------- + -------- + 3*|log(x)*sin(x) - ------|*|------ + cos(x)*log(x) + --------||
        |  \                  x   /                       x           3          2        \                  x   / |   2                        x    ||
        \                                                            x          x                                  \  x                              //
xcos⁡(x)(−(log⁡(x)sin⁡(x)−cos⁡(x)x)3+3(log⁡(x)sin⁡(x)−cos⁡(x)x)(log⁡(x)cos⁡(x)+2sin⁡(x)x+cos⁡(x)x2)+log⁡(x)sin⁡(x)−3cos⁡(x)x+3sin⁡(x)x2+2cos⁡(x)x3)x^{\cos{\left(x \right)}} \left(- \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right)^{3} + 3 \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x} + \frac{\cos{\left(x \right)}}{x^{2}}\right) + \log{\left(x \right)} \sin{\left(x \right)} - \frac{3 \cos{\left(x \right)}}{x} + \frac{3 \sin{\left(x \right)}}{x^{2}} + \frac{2 \cos{\left(x \right)}}{x^{3}}\right)
Simplificar
Gráfico
Derivada de x^cosx
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