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(п^2)/(arctg(e^x))
Derivada de la función/ arctg/ (п^2)/(arctg(e^x))

Derivada de (п^2)/(arctg(e^x))

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

Gráfico:

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Solución

Ha introducido [src] 
    2   
  pi    
--------
    / x\
atan\E /
π2atan⁡(ex)\frac{\pi^{2}}{\operatorname{atan}{\left(e^{x} \right)}} 
pi^2/atan(E^x)
Gráfica
02468-8-6-4-2-1010-500000500000
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Primera derivada [src] 
         2  x       
      -pi *e        
--------------------
/     2*x\     2/ x\
\1 + e   /*atan \E /
−π2ex(e2x+1)atan⁡2(ex)- \frac{\pi^{2} e^{x}}{\left(e^{2 x} + 1\right) \operatorname{atan}^{2}{\left(e^{x} \right)}}
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Segunda derivada [src] 
    /         2*x               x       \   
  2 |      2*e               2*e        |  x
pi *|-1 + -------- + -------------------|*e 
    |          2*x   /     2*x\     / x\|   
    \     1 + e      \1 + e   /*atan\E //   
--------------------------------------------
            /     2*x\     2/ x\            
            \1 + e   /*atan \E /
π2(−1+2e2xe2x+1+2ex(e2x+1)atan⁡(ex))ex(e2x+1)atan⁡2(ex)\frac{\pi^{2} \left(-1 + \frac{2 e^{2 x}}{e^{2 x} + 1} + \frac{2 e^{x}}{\left(e^{2 x} + 1\right) \operatorname{atan}{\left(e^{x} \right)}}\right) e^{x}}{\left(e^{2 x} + 1\right) \operatorname{atan}^{2}{\left(e^{x} \right)}}
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Tercera derivada [src] 
     /        2*x          4*x                x                     2*x                    3*x       \    
   2 |     8*e          8*e                6*e                   6*e                   12*e          |  x 
-pi *|1 - -------- + ----------- - ------------------- + --------------------- + --------------------|*e  
     |         2*x             2   /     2*x\     / x\             2                       2         |    
     |    1 + e      /     2*x\    \1 + e   /*atan\E /   /     2*x\      2/ x\   /     2*x\      / x\|    
     \               \1 + e   /                          \1 + e   / *atan \E /   \1 + e   / *atan\E //    
----------------------------------------------------------------------------------------------------------
                                           /     2*x\     2/ x\                                           
                                           \1 + e   /*atan \E /
−π2(1−8e2xe2x+1−6ex(e2x+1)atan⁡(ex)+8e4x(e2x+1)2+12e3x(e2x+1)2atan⁡(ex)+6e2x(e2x+1)2atan⁡2(ex))ex(e2x+1)atan⁡2(ex)- \frac{\pi^{2} \left(1 - \frac{8 e^{2 x}}{e^{2 x} + 1} - \frac{6 e^{x}}{\left(e^{2 x} + 1\right) \operatorname{atan}{\left(e^{x} \right)}} + \frac{8 e^{4 x}}{\left(e^{2 x} + 1\right)^{2}} + \frac{12 e^{3 x}}{\left(e^{2 x} + 1\right)^{2} \operatorname{atan}{\left(e^{x} \right)}} + \frac{6 e^{2 x}}{\left(e^{2 x} + 1\right)^{2} \operatorname{atan}^{2}{\left(e^{x} \right)}}\right) e^{x}}{\left(e^{2 x} + 1\right) \operatorname{atan}^{2}{\left(e^{x} \right)}}
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Gráfico
Derivada de (п^2)/(arctg(e^x))
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