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y=arctg^3(x+exp(x))=
Derivada de la función/ arctg/ x+exp/ exp(x)/ y=arctg^3(x+exp(x))=

Derivada de y=arctg^3(x+exp(x))=

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
    3/     x\
atan \x + e /
atan⁡3(x+ex)\operatorname{atan}^{3}{\left(x + e^{x} \right)} 
atan(x + exp(x))^3
Gráfica
02468-8-6-4-2-1010-1010
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Trazar el gráfico f'(x)
Primera derivada [src] 
      2/     x\ /     x\
3*atan \x + e /*\1 + e /
------------------------
                 2      
         /     x\       
     1 + \x + e /
3(ex+1)atan⁡2(x+ex)(x+ex)2+1\frac{3 \left(e^{x} + 1\right) \operatorname{atan}^{2}{\left(x + e^{x} \right)}}{\left(x + e^{x}\right)^{2} + 1}
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Segunda derivada [src] 
  /                             2              2                      \             
  |                     /     x\       /     x\  /     x\     /     x\|             
  |    /     x\  x    2*\1 + e /     2*\1 + e / *\x + e /*atan\x + e /|     /     x\
3*|atan\x + e /*e  + ------------- - ---------------------------------|*atan\x + e /
  |                              2                         2          |             
  |                      /     x\                  /     x\           |             
  \                  1 + \x + e /              1 + \x + e /           /             
------------------------------------------------------------------------------------
                                               2                                    
                                       /     x\                                     
                                   1 + \x + e /
3(−2(x+ex)(ex+1)2atan⁡(x+ex)(x+ex)2+1+exatan⁡(x+ex)+2(ex+1)2(x+ex)2+1)atan⁡(x+ex)(x+ex)2+1\frac{3 \left(- \frac{2 \left(x + e^{x}\right) \left(e^{x} + 1\right)^{2} \operatorname{atan}{\left(x + e^{x} \right)}}{\left(x + e^{x}\right)^{2} + 1} + e^{x} \operatorname{atan}{\left(x + e^{x} \right)} + \frac{2 \left(e^{x} + 1\right)^{2}}{\left(x + e^{x}\right)^{2} + 1}\right) \operatorname{atan}{\left(x + e^{x} \right)}}{\left(x + e^{x}\right)^{2} + 1}
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Tercera derivada [src] 
  /                               3                3                            3                                                                3         2                                                     \
  |                       /     x\         /     x\      2/     x\      /     x\  /     x\     /     x\     /     x\     /     x\  x     /     x\  /     x\      2/     x\         2/     x\ /     x\ /     x\  x|
  |    2/     x\  x     2*\1 + e /       2*\1 + e / *atan \x + e /   12*\1 + e / *\x + e /*atan\x + e /   6*\1 + e /*atan\x + e /*e    8*\1 + e / *\x + e / *atan \x + e /   6*atan \x + e /*\1 + e /*\x + e /*e |
3*|atan \x + e /*e  + ---------------- - ------------------------- - ---------------------------------- + -------------------------- + ----------------------------------- - ------------------------------------|
  |                                  2                     2                                 2                              2                                   2                                   2            |
  |                   /            2\              /     x\                   /            2\                       /     x\                     /            2\                            /     x\             |
  |                   |    /     x\ |          1 + \x + e /                   |    /     x\ |                   1 + \x + e /                     |    /     x\ |                        1 + \x + e /             |
  \                   \1 + \x + e / /                                         \1 + \x + e / /                                                    \1 + \x + e / /                                                 /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                              2                                                                                                   
                                                                                                      /     x\                                                                                                    
                                                                                                  1 + \x + e /
3(8(x+ex)2(ex+1)3atan⁡2(x+ex)((x+ex)2+1)2−6(x+ex)(ex+1)exatan⁡2(x+ex)(x+ex)2+1−12(x+ex)(ex+1)3atan⁡(x+ex)((x+ex)2+1)2+exatan⁡2(x+ex)−2(ex+1)3atan⁡2(x+ex)(x+ex)2+1+6(ex+1)exatan⁡(x+ex)(x+ex)2+1+2(ex+1)3((x+ex)2+1)2)(x+ex)2+1\frac{3 \left(\frac{8 \left(x + e^{x}\right)^{2} \left(e^{x} + 1\right)^{3} \operatorname{atan}^{2}{\left(x + e^{x} \right)}}{\left(\left(x + e^{x}\right)^{2} + 1\right)^{2}} - \frac{6 \left(x + e^{x}\right) \left(e^{x} + 1\right) e^{x} \operatorname{atan}^{2}{\left(x + e^{x} \right)}}{\left(x + e^{x}\right)^{2} + 1} - \frac{12 \left(x + e^{x}\right) \left(e^{x} + 1\right)^{3} \operatorname{atan}{\left(x + e^{x} \right)}}{\left(\left(x + e^{x}\right)^{2} + 1\right)^{2}} + e^{x} \operatorname{atan}^{2}{\left(x + e^{x} \right)} - \frac{2 \left(e^{x} + 1\right)^{3} \operatorname{atan}^{2}{\left(x + e^{x} \right)}}{\left(x + e^{x}\right)^{2} + 1} + \frac{6 \left(e^{x} + 1\right) e^{x} \operatorname{atan}{\left(x + e^{x} \right)}}{\left(x + e^{x}\right)^{2} + 1} + \frac{2 \left(e^{x} + 1\right)^{3}}{\left(\left(x + e^{x}\right)^{2} + 1\right)^{2}}\right)}{\left(x + e^{x}\right)^{2} + 1}
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Gráfico
Derivada de y=arctg^3(x+exp(x))=
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