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y=arcsin(x)/2^x

Derivada de y=arcsin(x)/2^x

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

Ha introducido [src]
asin(x)
-------
    x  
   2   
$$\frac{\operatorname{asin}{\left(x \right)}}{2^{x}}$$
asin(x)/2^x
Gráfica
Primera derivada [src]
     -x                         
    2          -x               
----------- - 2  *asin(x)*log(2)
   ________                     
  /      2                      
\/  1 - x                       
$$- 2^{- x} \log{\left(2 \right)} \operatorname{asin}{\left(x \right)} + \frac{2^{- x}}{\sqrt{1 - x^{2}}}$$
Segunda derivada [src]
 -x /     x           2                2*log(2) \
2  *|----------- + log (2)*asin(x) - -----------|
    |        3/2                        ________|
    |/     2\                          /      2 |
    \\1 - x /                        \/  1 - x  /
$$2^{- x} \left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \log{\left(2 \right)}^{2} \operatorname{asin}{\left(x \right)} - \frac{2 \log{\left(2 \right)}}{\sqrt{1 - x^{2}}}\right)$$
Tercera derivada [src]
    /            2                                               \
    |         3*x                                                |
    |  -1 + -------                                              |
    |             2                           2                  |
 -x |       -1 + x       3               3*log (2)     3*x*log(2)|
2  *|- ------------ - log (2)*asin(x) + ----------- - -----------|
    |          3/2                         ________           3/2|
    |  /     2\                           /      2    /     2\   |
    \  \1 - x /                         \/  1 - x     \1 - x /   /
$$2^{- x} \left(- \frac{3 x \log{\left(2 \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \log{\left(2 \right)}^{3} \operatorname{asin}{\left(x \right)} + \frac{3 \log{\left(2 \right)}^{2}}{\sqrt{1 - x^{2}}} - \frac{\frac{3 x^{2}}{x^{2} - 1} - 1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right)$$
Gráfico
Derivada de y=arcsin(x)/2^x