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(((е)^соsx)+arctgx)^3
Derivada de la función/ arctg/ (((е)^соsx)+arctgx)^3

Derivada de (((е)^соsx)+arctgx)^3

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
                   3
/ cos(x)          \ 
\E       + acot(x)/
(ecos⁡(x)+acot⁡(x))3\left(e^{\cos{\left(x \right)}} + \operatorname{acot}{\left(x \right)}\right)^{3} 
(E^cos(x) + acot(x))^3
Gráfica
02468-8-6-4-2-1010-200200
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Primera derivada [src] 
                   2                              
/ cos(x)          \  /    3         cos(x)       \
\E       + acot(x)/ *|- ------ - 3*e      *sin(x)|
                     |       2                   |
                     \  1 + x                    /
(ecos⁡(x)+acot⁡(x))2(−3ecos⁡(x)sin⁡(x)−3x2+1)\left(e^{\cos{\left(x \right)}} + \operatorname{acot}{\left(x \right)}\right)^{2} \left(- 3 e^{\cos{\left(x \right)}} \sin{\left(x \right)} - \frac{3}{x^{2} + 1}\right)
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Segunda derivada [src] 
  /                           2                                                                     \                    
  |  /  1       cos(x)       \    /           cos(x)\ /   2     cos(x)           cos(x)      2*x   \| /           cos(x)\
3*|2*|------ + e      *sin(x)|  + \acot(x) + e      /*|sin (x)*e       - cos(x)*e       + ---------||*\acot(x) + e      /
  |  |     2                 |                        |                                           2||                    
  |  \1 + x                  /                        |                                   /     2\ ||                    
  \                                                   \                                   \1 + x / //
3(2(ecos⁡(x)sin⁡(x)+1x2+1)2+(ecos⁡(x)+acot⁡(x))(2x(x2+1)2+ecos⁡(x)sin⁡2(x)−ecos⁡(x)cos⁡(x)))(ecos⁡(x)+acot⁡(x))3 \left(2 \left(e^{\cos{\left(x \right)}} \sin{\left(x \right)} + \frac{1}{x^{2} + 1}\right)^{2} + \left(e^{\cos{\left(x \right)}} + \operatorname{acot}{\left(x \right)}\right) \left(\frac{2 x}{\left(x^{2} + 1\right)^{2}} + e^{\cos{\left(x \right)}} \sin^{2}{\left(x \right)} - e^{\cos{\left(x \right)}} \cos{\left(x \right)}\right)\right) \left(e^{\cos{\left(x \right)}} + \operatorname{acot}{\left(x \right)}\right)
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Tercera derivada [src] 
  /                             3                      2 /                                                     2                            \                                                                                                 \
  |    /  1       cos(x)       \    /           cos(x)\  |    2        cos(x)             3     cos(x)      8*x                cos(x)       |     /  1       cos(x)       \ /           cos(x)\ /   2     cos(x)           cos(x)      2*x   \|
3*|- 2*|------ + e      *sin(x)|  + \acot(x) + e      / *|--------- + e      *sin(x) - sin (x)*e       - --------- + 3*cos(x)*e      *sin(x)| - 6*|------ + e      *sin(x)|*\acot(x) + e      /*|sin (x)*e       - cos(x)*e       + ---------||
  |    |     2                 |                         |        2                                              3                          |     |     2                 |                     |                                           2||
  |    \1 + x                  /                         |/     2\                                       /     2\                           |     \1 + x                  /                     |                                   /     2\ ||
  \                                                      \\1 + x /                                       \1 + x /                           /                                                   \                                   \1 + x / //
3(−2(ecos⁡(x)sin⁡(x)+1x2+1)3−6(ecos⁡(x)sin⁡(x)+1x2+1)(ecos⁡(x)+acot⁡(x))(2x(x2+1)2+ecos⁡(x)sin⁡2(x)−ecos⁡(x)cos⁡(x))+(ecos⁡(x)+acot⁡(x))2(−8x2(x2+1)3−ecos⁡(x)sin⁡3(x)+3ecos⁡(x)sin⁡(x)cos⁡(x)+ecos⁡(x)sin⁡(x)+2(x2+1)2))3 \left(- 2 \left(e^{\cos{\left(x \right)}} \sin{\left(x \right)} + \frac{1}{x^{2} + 1}\right)^{3} - 6 \left(e^{\cos{\left(x \right)}} \sin{\left(x \right)} + \frac{1}{x^{2} + 1}\right) \left(e^{\cos{\left(x \right)}} + \operatorname{acot}{\left(x \right)}\right) \left(\frac{2 x}{\left(x^{2} + 1\right)^{2}} + e^{\cos{\left(x \right)}} \sin^{2}{\left(x \right)} - e^{\cos{\left(x \right)}} \cos{\left(x \right)}\right) + \left(e^{\cos{\left(x \right)}} + \operatorname{acot}{\left(x \right)}\right)^{2} \left(- \frac{8 x^{2}}{\left(x^{2} + 1\right)^{3}} - e^{\cos{\left(x \right)}} \sin^{3}{\left(x \right)} + 3 e^{\cos{\left(x \right)}} \sin{\left(x \right)} \cos{\left(x \right)} + e^{\cos{\left(x \right)}} \sin{\left(x \right)} + \frac{2}{\left(x^{2} + 1\right)^{2}}\right)\right)
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Gráfico
Derivada de (((е)^соsx)+arctgx)^3
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