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y=arcsin(x)/sqrt(1-x^2)

Derivada de y=arcsin(x)/sqrt(1-x^2)

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

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Solución

Ha introducido [src]
  asin(x)  
-----------
   ________
  /      2 
\/  1 - x  
$$\frac{\operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}}$$
asin(x)/sqrt(1 - x^2)
Gráfica
Primera derivada [src]
           1               x*asin(x) 
----------------------- + -----------
   ________    ________           3/2
  /      2    /      2    /     2\   
\/  1 - x  *\/  1 - x     \1 - x /   
$$\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{1 - x^{2}} \sqrt{1 - x^{2}}}$$
Segunda derivada [src]
             /          2 \        
             |       3*x  |        
             |-1 + -------|*asin(x)
             |           2|        
   3*x       \     -1 + x /        
---------- - ----------------------
         2                3/2      
/      2\         /     2\         
\-1 + x /         \1 - x /         
$$\frac{3 x}{\left(x^{2} - 1\right)^{2}} - \frac{\left(\frac{3 x^{2}}{x^{2} - 1} - 1\right) \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}$$
Tercera derivada [src]
 /               /          2 \       /          2 \        \
 |               |       3*x  |       |       5*x  |        |
 |             4*|-1 + -------|   3*x*|-3 + -------|*asin(x)|
 |      2        |           2|       |           2|        |
 |   3*x         \     -1 + x /       \     -1 + x /        |
-|---------- + ---------------- + --------------------------|
 |         3               2                     5/2        |
 |/      2\       /      2\              /     2\           |
 \\-1 + x /       \-1 + x /              \1 - x /           /
$$- (\frac{3 x^{2}}{\left(x^{2} - 1\right)^{3}} + \frac{3 x \left(\frac{5 x^{2}}{x^{2} - 1} - 3\right) \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{4 \left(\frac{3 x^{2}}{x^{2} - 1} - 1\right)}{\left(x^{2} - 1\right)^{2}})$$
Gráfico
Derivada de y=arcsin(x)/sqrt(1-x^2)