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Derivada de z=y^arcsin^(2y+1)/3

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

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Definida a trozos:

Solución

Ha introducido [src]
     2*y + 1   
 asin       (3)
y              
$$y^{\operatorname{asin}^{2 y + 1}{\left(3 \right)}}$$
y^(asin(3)^(2*y + 1))
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

  2. Simplificamos:


Respuesta:

Primera derivada [src]
     2*y + 1    /    2*y + 1                                          \
 asin       (3) |asin       (3)         2*y + 1                       |
y              *|-------------- + 2*asin       (3)*log(y)*log(asin(3))|
                \      y                                              /
$$y^{\operatorname{asin}^{2 y + 1}{\left(3 \right)}} \left(2 \log{\left(y \right)} \log{\left(\operatorname{asin}{\left(3 \right)} \right)} \operatorname{asin}^{2 y + 1}{\left(3 \right)} + \frac{\operatorname{asin}^{2 y + 1}{\left(3 \right)}}{y}\right)$$
Segunda derivada [src]
     1 + 2*y    /                           2                                                                                 \
 asin       (3) |/1                        \      2 + 4*y          1 + 2*y    /  1    4*log(asin(3))        2                \|
y              *||- + 2*log(y)*log(asin(3))| *asin       (3) + asin       (3)*|- -- + -------------- + 4*log (asin(3))*log(y)||
                |\y                        /                                  |   2         y                                ||
                \                                                             \  y                                           //
$$y^{\operatorname{asin}^{2 y + 1}{\left(3 \right)}} \left(\left(2 \log{\left(y \right)} \log{\left(\operatorname{asin}{\left(3 \right)} \right)} + \frac{1}{y}\right)^{2} \operatorname{asin}^{4 y + 2}{\left(3 \right)} + \left(4 \log{\left(y \right)} \log{\left(\operatorname{asin}{\left(3 \right)} \right)}^{2} + \frac{4 \log{\left(\operatorname{asin}{\left(3 \right)} \right)}}{y} - \frac{1}{y^{2}}\right) \operatorname{asin}^{2 y + 1}{\left(3 \right)}\right)$$
Tercera derivada [src]
     1 + 2*y    /                           3                                   /                                                    2         \                                                                                                \
 asin       (3) |/1                        \      3 + 6*y            1 + 2*y    |1    3*log(asin(3))        3                   6*log (asin(3))|         2 + 4*y    /1                        \ /  1    4*log(asin(3))        2                \|
y              *||- + 2*log(y)*log(asin(3))| *asin       (3) + 2*asin       (3)*|-- - -------------- + 4*log (asin(3))*log(y) + ---------------| + 3*asin       (3)*|- + 2*log(y)*log(asin(3))|*|- -- + -------------- + 4*log (asin(3))*log(y)||
                |\y                        /                                    | 3          2                                         y       |                    \y                        / |   2         y                                ||
                \                                                               \y          y                                                  /                                                \  y                                           //
$$y^{\operatorname{asin}^{2 y + 1}{\left(3 \right)}} \left(\left(2 \log{\left(y \right)} \log{\left(\operatorname{asin}{\left(3 \right)} \right)} + \frac{1}{y}\right)^{3} \operatorname{asin}^{6 y + 3}{\left(3 \right)} + 3 \left(2 \log{\left(y \right)} \log{\left(\operatorname{asin}{\left(3 \right)} \right)} + \frac{1}{y}\right) \left(4 \log{\left(y \right)} \log{\left(\operatorname{asin}{\left(3 \right)} \right)}^{2} + \frac{4 \log{\left(\operatorname{asin}{\left(3 \right)} \right)}}{y} - \frac{1}{y^{2}}\right) \operatorname{asin}^{4 y + 2}{\left(3 \right)} + 2 \left(4 \log{\left(y \right)} \log{\left(\operatorname{asin}{\left(3 \right)} \right)}^{3} + \frac{6 \log{\left(\operatorname{asin}{\left(3 \right)} \right)}^{2}}{y} - \frac{3 \log{\left(\operatorname{asin}{\left(3 \right)} \right)}}{y^{2}} + \frac{1}{y^{3}}\right) \operatorname{asin}^{2 y + 1}{\left(3 \right)}\right)$$