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y=e^sinx×arctg4x
Derivada de la función/ ctg4x/ arctg/ e^sinx/ y=e^sinx×arctg4x

Derivada de y=e^sinx×arctg4x

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

Ha introducido [src] 
 sin(x)          
E      *atan(4*x)
esin⁡(x)atan⁡(4x)e^{\sin{\left(x \right)}} \operatorname{atan}{\left(4 x \right)} 
E^sin(x)*atan(4*x)
Gráfica
02468-8-6-4-2-1010-1010
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Primera derivada [src] 
   sin(x)                           
4*e                           sin(x)
--------- + atan(4*x)*cos(x)*e      
        2                           
1 + 16*x
esin⁡(x)cos⁡(x)atan⁡(4x)+4esin⁡(x)16x2+1e^{\sin{\left(x \right)}} \cos{\left(x \right)} \operatorname{atan}{\left(4 x \right)} + \frac{4 e^{\sin{\left(x \right)}}}{16 x^{2} + 1}
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Segunda derivada [src] 
/  /     2            \                128*x        8*cos(x)\  sin(x)
|- \- cos (x) + sin(x)/*atan(4*x) - ------------ + ---------|*e      
|                                              2           2|        
|                                   /        2\    1 + 16*x |        
\                                   \1 + 16*x /             /
(−128x(16x2+1)2−(sin⁡(x)−cos⁡2(x))atan⁡(4x)+8cos⁡(x)16x2+1)esin⁡(x)\left(- \frac{128 x}{\left(16 x^{2} + 1\right)^{2}} - \left(\sin{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \operatorname{atan}{\left(4 x \right)} + \frac{8 \cos{\left(x \right)}}{16 x^{2} + 1}\right) e^{\sin{\left(x \right)}}
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Tercera derivada [src] 
/                                /           2  \                                                           \        
|                                |       64*x   |                                                           |        
|                            128*|-1 + ---------|                                                           |        
|     /     2            \       |             2|                                                           |        
|  12*\- cos (x) + sin(x)/       \     1 + 16*x /   /       2              \                    384*x*cos(x)|  sin(x)
|- ----------------------- + -------------------- - \1 - cos (x) + 3*sin(x)/*atan(4*x)*cos(x) - ------------|*e      
|                 2                         2                                                              2|        
|         1 + 16*x               /        2\                                                    /        2\ |        
\                                \1 + 16*x /                                                    \1 + 16*x / /
(−384xcos⁡(x)(16x2+1)2−(3sin⁡(x)−cos⁡2(x)+1)cos⁡(x)atan⁡(4x)−12(sin⁡(x)−cos⁡2(x))16x2+1+128(64x216x2+1−1)(16x2+1)2)esin⁡(x)\left(- \frac{384 x \cos{\left(x \right)}}{\left(16 x^{2} + 1\right)^{2}} - \left(3 \sin{\left(x \right)} - \cos^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)} \operatorname{atan}{\left(4 x \right)} - \frac{12 \left(\sin{\left(x \right)} - \cos^{2}{\left(x \right)}\right)}{16 x^{2} + 1} + \frac{128 \left(\frac{64 x^{2}}{16 x^{2} + 1} - 1\right)}{\left(16 x^{2} + 1\right)^{2}}\right) e^{\sin{\left(x \right)}}
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Gráfico
Derivada de y=e^sinx×arctg4x
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