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е^(cosx)*arcsinx
Derivada de la función/ arcsin/ е^(cosx)/ е^(cosx)*arcsinx

Derivada de е^(cosx)*arcsinx

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

Gráfico:

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Solución

Ha introducido [src] 
 cos(x)        
E      *asin(x)
ecos⁡(x)asin⁡(x)e^{\cos{\left(x \right)}} \operatorname{asin}{\left(x \right)} 
E^cos(x)*asin(x)
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
   cos(x)                           
  e                    cos(x)       
----------- - asin(x)*e      *sin(x)
   ________                         
  /      2                          
\/  1 - x
−ecos⁡(x)sin⁡(x)asin⁡(x)+ecos⁡(x)1−x2- e^{\cos{\left(x \right)}} \sin{\left(x \right)} \operatorname{asin}{\left(x \right)} + \frac{e^{\cos{\left(x \right)}}}{\sqrt{1 - x^{2}}}
Simplificar
Segunda derivada [src] 
/     x        /   2            \             2*sin(x) \  cos(x)
|----------- + \sin (x) - cos(x)/*asin(x) - -----------|*e      
|        3/2                                   ________|        
|/     2\                                     /      2 |        
\\1 - x /                                   \/  1 - x  /
(x(1−x2)32+(sin⁡2(x)−cos⁡(x))asin⁡(x)−2sin⁡(x)1−x2)ecos⁡(x)\left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \left(\sin^{2}{\left(x \right)} - \cos{\left(x \right)}\right) \operatorname{asin}{\left(x \right)} - \frac{2 \sin{\left(x \right)}}{\sqrt{1 - x^{2}}}\right) e^{\cos{\left(x \right)}}
Simplificar
Tercera derivada [src] 
/            2                                                                                \        
|         3*x                                                                                 |        
|  -1 + -------                                                                               |        
|             2     /   2            \                                                        |        
|       -1 + x    3*\sin (x) - cos(x)/   /       2              \                   3*x*sin(x)|  cos(x)
|- ------------ + -------------------- + \1 - sin (x) + 3*cos(x)/*asin(x)*sin(x) - -----------|*e      
|          3/2           ________                                                          3/2|        
|  /     2\             /      2                                                   /     2\   |        
\  \1 - x /           \/  1 - x                                                    \1 - x /   /
(−3xsin⁡(x)(1−x2)32+(−sin⁡2(x)+3cos⁡(x)+1)sin⁡(x)asin⁡(x)+3(sin⁡2(x)−cos⁡(x))1−x2−3x2x2−1−1(1−x2)32)ecos⁡(x)\left(- \frac{3 x \sin{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \left(- \sin^{2}{\left(x \right)} + 3 \cos{\left(x \right)} + 1\right) \sin{\left(x \right)} \operatorname{asin}{\left(x \right)} + \frac{3 \left(\sin^{2}{\left(x \right)} - \cos{\left(x \right)}\right)}{\sqrt{1 - x^{2}}} - \frac{\frac{3 x^{2}}{x^{2} - 1} - 1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) e^{\cos{\left(x \right)}}
Simplificar
Gráfico
Derivada de е^(cosx)*arcsinx
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