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y=(1+cosx)^(ln^(2)x)

Derivada de y=(1+cosx)^(ln^(2)x)

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

Ha introducido [src]
               2   
            log (x)
(1 + cos(x))       
$$\left(\cos{\left(x \right)} + 1\right)^{\log{\left(x \right)}^{2}}$$
(1 + cos(x))^(log(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                                     \
            log (x) |  log (x)*sin(x)   2*log(x)*log(1 + cos(x))|
(1 + cos(x))       *|- -------------- + ------------------------|
                    \    1 + cos(x)                x            /
$$\left(- \frac{\log{\left(x \right)}^{2} \sin{\left(x \right)}}{\cos{\left(x \right)} + 1} + \frac{2 \log{\left(x \right)} \log{\left(\cos{\left(x \right)} + 1 \right)}}{x}\right) \left(\cos{\left(x \right)} + 1\right)^{\log{\left(x \right)}^{2}}$$
Segunda derivada [src]
               2    /                                     2                                  2                2       2                                                \
            log (x) |/  2*log(1 + cos(x))   log(x)*sin(x)\     2      2*log(1 + cos(x))   log (x)*cos(x)   log (x)*sin (x)   2*log(x)*log(1 + cos(x))   4*log(x)*sin(x)|
(1 + cos(x))       *||- ----------------- + -------------| *log (x) + ----------------- - -------------- - --------------- - ------------------------ - ---------------|
                    |\          x             1 + cos(x) /                     2            1 + cos(x)                  2                2               x*(1 + cos(x))|
                    \                                                         x                             (1 + cos(x))                x                              /
$$\left(\cos{\left(x \right)} + 1\right)^{\log{\left(x \right)}^{2}} \left(\left(\frac{\log{\left(x \right)} \sin{\left(x \right)}}{\cos{\left(x \right)} + 1} - \frac{2 \log{\left(\cos{\left(x \right)} + 1 \right)}}{x}\right)^{2} \log{\left(x \right)}^{2} - \frac{\log{\left(x \right)}^{2} \cos{\left(x \right)}}{\cos{\left(x \right)} + 1} - \frac{\log{\left(x \right)}^{2} \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2}} - \frac{4 \log{\left(x \right)} \sin{\left(x \right)}}{x \left(\cos{\left(x \right)} + 1\right)} - \frac{2 \log{\left(x \right)} \log{\left(\cos{\left(x \right)} + 1 \right)}}{x^{2}} + \frac{2 \log{\left(\cos{\left(x \right)} + 1 \right)}}{x^{2}}\right)$$
Tercera derivada [src]
               2    /                                       3                                  2                                    2       3                                              /                         2                2       2                                                \                                                            2                  2                                   \
            log (x) |  /  2*log(1 + cos(x))   log(x)*sin(x)\     3      6*log(1 + cos(x))   log (x)*sin(x)       6*sin(x)      2*log (x)*sin (x)     /  2*log(1 + cos(x))   log(x)*sin(x)\ |  2*log(1 + cos(x))   log (x)*cos(x)   log (x)*sin (x)   2*log(x)*log(1 + cos(x))   4*log(x)*sin(x)|          4*log(x)*log(1 + cos(x))   6*cos(x)*log(x)   6*sin (x)*log(x)   3*log (x)*cos(x)*sin(x)   6*log(x)*sin(x)|
(1 + cos(x))       *|- |- ----------------- + -------------| *log (x) - ----------------- + -------------- - --------------- - ----------------- + 3*|- ----------------- + -------------|*|- ----------------- + -------------- + --------------- + ------------------------ + ---------------|*log(x) + ------------------------ - --------------- - ---------------- - ----------------------- + ---------------|
                    |  \          x             1 + cos(x) /                     3            1 + cos(x)      2                              3       \          x             1 + cos(x) / |           2            1 + cos(x)                  2                2               x*(1 + cos(x))|                      3               x*(1 + cos(x))                 2                     2         2             |
                    \                                                           x                            x *(1 + cos(x))     (1 + cos(x))                                              \          x                             (1 + cos(x))                x                              /                     x                                 x*(1 + cos(x))          (1 + cos(x))         x *(1 + cos(x))/
$$\left(\cos{\left(x \right)} + 1\right)^{\log{\left(x \right)}^{2}} \left(- \left(\frac{\log{\left(x \right)} \sin{\left(x \right)}}{\cos{\left(x \right)} + 1} - \frac{2 \log{\left(\cos{\left(x \right)} + 1 \right)}}{x}\right)^{3} \log{\left(x \right)}^{3} + 3 \left(\frac{\log{\left(x \right)} \sin{\left(x \right)}}{\cos{\left(x \right)} + 1} - \frac{2 \log{\left(\cos{\left(x \right)} + 1 \right)}}{x}\right) \left(\frac{\log{\left(x \right)}^{2} \cos{\left(x \right)}}{\cos{\left(x \right)} + 1} + \frac{\log{\left(x \right)}^{2} \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2}} + \frac{4 \log{\left(x \right)} \sin{\left(x \right)}}{x \left(\cos{\left(x \right)} + 1\right)} + \frac{2 \log{\left(x \right)} \log{\left(\cos{\left(x \right)} + 1 \right)}}{x^{2}} - \frac{2 \log{\left(\cos{\left(x \right)} + 1 \right)}}{x^{2}}\right) \log{\left(x \right)} + \frac{\log{\left(x \right)}^{2} \sin{\left(x \right)}}{\cos{\left(x \right)} + 1} - \frac{3 \log{\left(x \right)}^{2} \sin{\left(x \right)} \cos{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2}} - \frac{2 \log{\left(x \right)}^{2} \sin^{3}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{3}} - \frac{6 \log{\left(x \right)} \cos{\left(x \right)}}{x \left(\cos{\left(x \right)} + 1\right)} - \frac{6 \log{\left(x \right)} \sin^{2}{\left(x \right)}}{x \left(\cos{\left(x \right)} + 1\right)^{2}} + \frac{6 \log{\left(x \right)} \sin{\left(x \right)}}{x^{2} \left(\cos{\left(x \right)} + 1\right)} - \frac{6 \sin{\left(x \right)}}{x^{2} \left(\cos{\left(x \right)} + 1\right)} + \frac{4 \log{\left(x \right)} \log{\left(\cos{\left(x \right)} + 1 \right)}}{x^{3}} - \frac{6 \log{\left(\cos{\left(x \right)} + 1 \right)}}{x^{3}}\right)$$
Gráfico
Derivada de y=(1+cosx)^(ln^(2)x)