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y=(cosx)^x^2

Derivada de y=(cosx)^x^2

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src]
        / 2\
        \x /
(cos(x))    
$$\cos^{x^{2}}{\left(x \right)}$$
cos(x)^(x^2)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada


Respuesta:

Gráfica
Primera derivada [src]
        / 2\ /                   2       \
        \x / |                  x *sin(x)|
(cos(x))    *|2*x*log(cos(x)) - ---------|
             \                    cos(x) /
$$\left(- \frac{x^{2} \sin{\left(x \right)}}{\cos{\left(x \right)}} + 2 x \log{\left(\cos{\left(x \right)} \right)}\right) \cos^{x^{2}}{\left(x \right)}$$
Segunda derivada [src]
        / 2\ /                                                     2    2    2                \
        \x / |   2                    2 /                 x*sin(x)\    x *sin (x)   4*x*sin(x)|
(cos(x))    *|- x  + 2*log(cos(x)) + x *|-2*log(cos(x)) + --------|  - ---------- - ----------|
             |                          \                  cos(x) /        2          cos(x)  |
             \                                                          cos (x)               /
$$\left(x^{2} \left(\frac{x \sin{\left(x \right)}}{\cos{\left(x \right)}} - 2 \log{\left(\cos{\left(x \right)} \right)}\right)^{2} - \frac{x^{2} \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} - x^{2} - \frac{4 x \sin{\left(x \right)}}{\cos{\left(x \right)}} + 2 \log{\left(\cos{\left(x \right)} \right)}\right) \cos^{x^{2}}{\left(x \right)}$$
Tercera derivada [src]
        / 2\ /                                     3                     2         2             2    3                                      /                      2    2                \\
        \x / |        3 /                 x*sin(x)\    6*sin(x)   6*x*sin (x)   2*x *sin(x)   2*x *sin (x)       /                 x*sin(x)\ | 2                   x *sin (x)   4*x*sin(x)||
(cos(x))    *|-6*x - x *|-2*log(cos(x)) + --------|  - -------- - ----------- - ----------- - ------------ + 3*x*|-2*log(cos(x)) + --------|*|x  - 2*log(cos(x)) + ---------- + ----------||
             |          \                  cos(x) /     cos(x)         2           cos(x)          3             \                  cos(x) / |                         2          cos(x)  ||
             \                                                      cos (x)                     cos (x)                                      \                      cos (x)               //
$$\left(- x^{3} \left(\frac{x \sin{\left(x \right)}}{\cos{\left(x \right)}} - 2 \log{\left(\cos{\left(x \right)} \right)}\right)^{3} - \frac{2 x^{2} \sin^{3}{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{2 x^{2} \sin{\left(x \right)}}{\cos{\left(x \right)}} + 3 x \left(\frac{x \sin{\left(x \right)}}{\cos{\left(x \right)}} - 2 \log{\left(\cos{\left(x \right)} \right)}\right) \left(\frac{x^{2} \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + x^{2} + \frac{4 x \sin{\left(x \right)}}{\cos{\left(x \right)}} - 2 \log{\left(\cos{\left(x \right)} \right)}\right) - \frac{6 x \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} - 6 x - \frac{6 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right) \cos^{x^{2}}{\left(x \right)}$$
Gráfico
Derivada de y=(cosx)^x^2