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Derivada de la función/ x^e^x/ tg(x)/ y=x^e/ arctg/ y=x^e^x*arctg(x)

Derivada de y=x^e^x*arctg(x)

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

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Solución

Ha introducido [src] 
 / x\        
 \E /        
x    *atan(x)
xexatan⁡(x)x^{e^{x}} \operatorname{atan}{\left(x \right)} 
x^(E^x)*atan(x)
Primera derivada [src] 
 / x\                                  
 \E /     / x\ / x            \        
x         \E / |e     x       |        
------ + x    *|-- + e *log(x)|*atan(x)
     2         \x             /        
1 + x
xex(exlog⁡(x)+exx)atan⁡(x)+xexx2+1x^{e^{x}} \left(e^{x} \log{\left(x \right)} + \frac{e^{x}}{x}\right) \operatorname{atan}{\left(x \right)} + \frac{x^{e^{x}}}{x^{2} + 1}
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Segunda derivada [src] 
      /                                                                    /1         \  x\
 / x\ |              /                       2            \              2*|- + log(x)|*e |
 \e / |     2*x      |  1    2   /1         \   x         |          x     \x         /   |
x    *|- --------- + |- -- + - + |- + log(x)| *e  + log(x)|*atan(x)*e  + -----------------|
      |          2   |   2   x   \x         /             |                         2     |
      |  /     2\    \  x                                 /                    1 + x      |
      \  \1 + x /                                                                         /
xex(−2x(x2+1)2+((log⁡(x)+1x)2ex+log⁡(x)+2x−1x2)exatan⁡(x)+2(log⁡(x)+1x)exx2+1)x^{e^{x}} \left(- \frac{2 x}{\left(x^{2} + 1\right)^{2}} + \left(\left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{x} + \log{\left(x \right)} + \frac{2}{x} - \frac{1}{x^{2}}\right) e^{x} \operatorname{atan}{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x}}{x^{2} + 1}\right)
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Tercera derivada [src] 
      /  /         2 \                                                                                                        /                       2            \                         \
      |  |      4*x  |                                                                                                        |  1    2   /1         \   x         |  x                      |
      |2*|-1 + ------|                                                                                                      3*|- -- + - + |- + log(x)| *e  + log(x)|*e        /1         \  x|
 / x\ |  |          2|   /                            3                                                      \                |   2   x   \x         /             |      6*x*|- + log(x)|*e |
 \e / |  \     1 + x /   |  3    2    3   /1         \   2*x     /1         \ /  1    2         \  x         |          x     \  x                                 /          \x         /   |
x    *|--------------- + |- -- + -- + - + |- + log(x)| *e    + 3*|- + log(x)|*|- -- + - + log(x)|*e  + log(x)|*atan(x)*e  + ------------------------------------------- - -------------------|
      |           2      |   2    3   x   \x         /           \x         / |   2   x         |            |                                      2                                  2     |
      |   /     2\       \  x    x                                            \  x              /            /                                 1 + x                           /     2\      |
      \   \1 + x /                                                                                                                                                             \1 + x /      /
xex(−6x(log⁡(x)+1x)ex(x2+1)2+((log⁡(x)+1x)3e2x+3(log⁡(x)+1x)(log⁡(x)+2x−1x2)ex+log⁡(x)+3x−3x2+2x3)exatan⁡(x)+3((log⁡(x)+1x)2ex+log⁡(x)+2x−1x2)exx2+1+2(4x2x2+1−1)(x2+1)2)x^{e^{x}} \left(- \frac{6 x \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x}}{\left(x^{2} + 1\right)^{2}} + \left(\left(\log{\left(x \right)} + \frac{1}{x}\right)^{3} e^{2 x} + 3 \left(\log{\left(x \right)} + \frac{1}{x}\right) \left(\log{\left(x \right)} + \frac{2}{x} - \frac{1}{x^{2}}\right) e^{x} + \log{\left(x \right)} + \frac{3}{x} - \frac{3}{x^{2}} + \frac{2}{x^{3}}\right) e^{x} \operatorname{atan}{\left(x \right)} + \frac{3 \left(\left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{x} + \log{\left(x \right)} + \frac{2}{x} - \frac{1}{x^{2}}\right) e^{x}}{x^{2} + 1} + \frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}}\right)
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