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y=e^sinx*arctg3x
Derivada de la función/ arctg/ ctg3x/ e^sinx/ y=e^sinx*arctg3x

Derivada de y=e^sinx*arctg3x

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

Ha introducido [src] 
 sin(x)          
E      *atan(3*x)
esin⁡(x)atan⁡(3x)e^{\sin{\left(x \right)}} \operatorname{atan}{\left(3 x \right)} 
E^sin(x)*atan(3*x)
Gráfica
02468-8-6-4-2-1010-1010
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Trazar el gráfico f'(x)
Primera derivada [src] 
   sin(x)                           
3*e                           sin(x)
--------- + atan(3*x)*cos(x)*e      
        2                           
 1 + 9*x
esin⁡(x)cos⁡(x)atan⁡(3x)+3esin⁡(x)9x2+1e^{\sin{\left(x \right)}} \cos{\left(x \right)} \operatorname{atan}{\left(3 x \right)} + \frac{3 e^{\sin{\left(x \right)}}}{9 x^{2} + 1}
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Segunda derivada [src] 
/  /     2            \                 54*x      6*cos(x)\  sin(x)
|- \- cos (x) + sin(x)/*atan(3*x) - ----------- + --------|*e      
|                                             2          2|        
|                                   /       2\    1 + 9*x |        
\                                   \1 + 9*x /            /
(−54x(9x2+1)2−(sin⁡(x)−cos⁡2(x))atan⁡(3x)+6cos⁡(x)9x2+1)esin⁡(x)\left(- \frac{54 x}{\left(9 x^{2} + 1\right)^{2}} - \left(\sin{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \operatorname{atan}{\left(3 x \right)} + \frac{6 \cos{\left(x \right)}}{9 x^{2} + 1}\right) e^{\sin{\left(x \right)}}
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Tercera derivada [src] 
/                              /          2  \                                                           \        
|                              |      36*x   |                                                           |        
|                           54*|-1 + --------|                                                           |        
|    /     2            \      |            2|                                                           |        
|  9*\- cos (x) + sin(x)/      \     1 + 9*x /   /       2              \                    162*x*cos(x)|  sin(x)
|- ---------------------- + ------------------ - \1 - cos (x) + 3*sin(x)/*atan(3*x)*cos(x) - ------------|*e      
|                2                       2                                                             2 |        
|         1 + 9*x              /       2\                                                    /       2\  |        
\                              \1 + 9*x /                                                    \1 + 9*x /  /
(−162xcos⁡(x)(9x2+1)2−(3sin⁡(x)−cos⁡2(x)+1)cos⁡(x)atan⁡(3x)−9(sin⁡(x)−cos⁡2(x))9x2+1+54(36x29x2+1−1)(9x2+1)2)esin⁡(x)\left(- \frac{162 x \cos{\left(x \right)}}{\left(9 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(3 x \right)} - \frac{9 \left(\sin{\left(x \right)} - \cos^{2}{\left(x \right)}\right)}{9 x^{2} + 1} + \frac{54 \left(\frac{36 x^{2}}{9 x^{2} + 1} - 1\right)}{\left(9 x^{2} + 1\right)^{2}}\right) e^{\sin{\left(x \right)}}
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Gráfico
Derivada de y=e^sinx*arctg3x
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