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y=arcsin(e^sinx)
Derivada de la función/ e^sinx/ arcsin/ y=arcsin(e^sinx)

Derivada de y=arcsin(e^sinx)

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

Ha introducido [src] 
    / sin(x)\
asin\E      /
asin⁡(esin⁡(x))\operatorname{asin}{\left(e^{\sin{\left(x \right)}} \right)} 
asin(E^sin(x))
Gráfica
02468-8-6-4-2-1010-1010
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
          sin(x)  
  cos(x)*e        
------------------
   _______________
  /      2*sin(x) 
\/  1 - e
esin⁡(x)cos⁡(x)1−e2sin⁡(x)\frac{e^{\sin{\left(x \right)}} \cos{\left(x \right)}}{\sqrt{1 - e^{2 \sin{\left(x \right)}}}}
Simplificar
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
(−sin⁡(x)+cos⁡2(x)+e2sin⁡(x)cos⁡2(x)1−e2sin⁡(x))esin⁡(x)1−e2sin⁡(x)\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)}}}}
Simplificar
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
(−3sin⁡(x)+cos⁡2(x)−1−3e2sin⁡(x)sin⁡(x)1−e2sin⁡(x)+4e2sin⁡(x)cos⁡2(x)1−e2sin⁡(x)+3e4sin⁡(x)cos⁡2(x)(1−e2sin⁡(x))2)esin⁡(x)cos⁡(x)1−e2sin⁡(x)\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)}}}}
Simplificar
Gráfico
Derivada de y=arcsin(e^sinx)
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