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Derivada de la función/ (x^3)/ cos6x/ y=(cos6x)^(x^3)

Derivada de y=(cos6x)^(x^3)

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

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Solución

Ha introducido [src] 
          / 3\
          \x /
(cos(6*x))
$$\cos^{x^{3}}{\left(6 x \right)}$$ 
cos(6*x)^(x^3)
Solución detallada

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

    Perola derivada

Respuesta:

Primera derivada [src] 
          / 3\ /                        3         \
          \x / |   2                 6*x *sin(6*x)|
(cos(6*x))    *|3*x *log(cos(6*x)) - -------------|
               \                        cos(6*x)  /
$$\left(- \frac{6 x^{3} \sin{\left(6 x \right)}}{\cos{\left(6 x \right)}} + 3 x^{2} \log{\left(\cos{\left(6 x \right)} \right)}\right) \cos^{x^{3}}{\left(6 x \right)}$$
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Segunda derivada [src] 
              / 3\ /                                                                2                       2    2     \
              \x / |      2                        3 /                 2*x*sin(6*x)\    12*x*sin(6*x)   12*x *sin (6*x)|
3*x*(cos(6*x))    *|- 12*x  + 2*log(cos(6*x)) + 3*x *|-log(cos(6*x)) + ------------|  - ------------- - ---------------|
                   |                                 \                   cos(6*x)  /       cos(6*x)           2        |
                   \                                                                                       cos (6*x)   /
$$3 x \left(3 x^{3} \left(\frac{2 x \sin{\left(6 x \right)}}{\cos{\left(6 x \right)}} - \log{\left(\cos{\left(6 x \right)} \right)}\right)^{2} - \frac{12 x^{2} \sin^{2}{\left(6 x \right)}}{\cos^{2}{\left(6 x \right)}} - 12 x^{2} - \frac{12 x \sin{\left(6 x \right)}}{\cos{\left(6 x \right)}} + 2 \log{\left(\cos{\left(6 x \right)} \right)}\right) \cos^{x^{3}}{\left(6 x \right)}$$
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Tercera derivada [src] 
            / 3\ /                                                                 3        3                 3    3             2    2                                                              /                                          2    2     \\
            \x / |       2                        6 /                 2*x*sin(6*x)\    144*x *sin(6*x)   144*x *sin (6*x)   108*x *sin (6*x)   36*x*sin(6*x)       3 /                 2*x*sin(6*x)\ |                    2   6*x*sin(6*x)   6*x *sin (6*x)||
3*(cos(6*x))    *|- 108*x  + 2*log(cos(6*x)) - 9*x *|-log(cos(6*x)) + ------------|  - --------------- - ---------------- - ---------------- - ------------- + 18*x *|-log(cos(6*x)) + ------------|*|-log(cos(6*x)) + 6*x  + ------------ + --------------||
                 |                                  \                   cos(6*x)  /        cos(6*x)            3                  2               cos(6*x)           \                   cos(6*x)  / |                          cos(6*x)          2        ||
                 \                                                                                          cos (6*x)          cos (6*x)                                                             \                                         cos (6*x)   //
$$3 \left(- 9 x^{6} \left(\frac{2 x \sin{\left(6 x \right)}}{\cos{\left(6 x \right)}} - \log{\left(\cos{\left(6 x \right)} \right)}\right)^{3} + 18 x^{3} \left(\frac{2 x \sin{\left(6 x \right)}}{\cos{\left(6 x \right)}} - \log{\left(\cos{\left(6 x \right)} \right)}\right) \left(\frac{6 x^{2} \sin^{2}{\left(6 x \right)}}{\cos^{2}{\left(6 x \right)}} + 6 x^{2} + \frac{6 x \sin{\left(6 x \right)}}{\cos{\left(6 x \right)}} - \log{\left(\cos{\left(6 x \right)} \right)}\right) - \frac{144 x^{3} \sin^{3}{\left(6 x \right)}}{\cos^{3}{\left(6 x \right)}} - \frac{144 x^{3} \sin{\left(6 x \right)}}{\cos{\left(6 x \right)}} - \frac{108 x^{2} \sin^{2}{\left(6 x \right)}}{\cos^{2}{\left(6 x \right)}} - 108 x^{2} - \frac{36 x \sin{\left(6 x \right)}}{\cos{\left(6 x \right)}} + 2 \log{\left(\cos{\left(6 x \right)} \right)}\right) \cos^{x^{3}}{\left(6 x \right)}$$
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