Sr Examen

Derivada de ln(arcsinx)

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

Gráfico:

interior superior

Definida a trozos:

Solución

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