Sr Examen

Derivada de y=arcsin^4x

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src]
    4   
asin (x)
$$\operatorname{asin}^{4}{\left(x \right)}$$
asin(x)^4
Gráfica
Primera derivada [src]
       3   
 4*asin (x)
-----------
   ________
  /      2 
\/  1 - x  
$$\frac{4 \operatorname{asin}^{3}{\left(x \right)}}{\sqrt{1 - x^{2}}}$$
Segunda derivada [src]
      2    /     3       x*asin(x) \
4*asin (x)*|- ------- + -----------|
           |        2           3/2|
           |  -1 + x    /     2\   |
           \            \1 - x /   /
$$4 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{3}{x^{2} - 1}\right) \operatorname{asin}^{2}{\left(x \right)}$$
Tercera derivada [src]
  /                    2          2     2                 \        
  |     6          asin (x)    3*x *asin (x)   9*x*asin(x)|        
4*|----------- + ----------- + ------------- + -----------|*asin(x)
  |        3/2           3/2            5/2              2|        
  |/     2\      /     2\       /     2\        /      2\ |        
  \\1 - x /      \1 - x /       \1 - x /        \-1 + x / /        
$$4 \left(\frac{3 x^{2} \operatorname{asin}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{9 x \operatorname{asin}{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{6}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \operatorname{asin}{\left(x \right)}$$
Gráfico
Derivada de y=arcsin^4x