Sr Examen

Derivada de y=arcsin(e^sinx)

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

Gráfico:

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Definida a trozos:

Solución

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