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y=e^arctg^2(2x-1)
Derivada de la función/ ctg^2/ arctg/ (2x-1)/ y=e^arctg^2(2x-1)

Derivada de y=e^arctg^2(2x-1)

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

Gráfico:

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Solución

Ha introducido [src] 
     2         
 atan (2*x - 1)
E
eatan⁡2(2x−1)e^{\operatorname{atan}^{2}{\left(2 x - 1 \right)}} 
E^(atan(2*x - 1)^2)
Gráfica
02468-8-6-4-2-101020-10
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Trazar el gráfico f'(x)
Primera derivada [src] 
                     2         
                 atan (2*x - 1)
4*atan(2*x - 1)*e              
-------------------------------
                      2        
         1 + (2*x - 1)
4eatan⁡2(2x−1)atan⁡(2x−1)(2x−1)2+1\frac{4 e^{\operatorname{atan}^{2}{\left(2 x - 1 \right)}} \operatorname{atan}{\left(2 x - 1 \right)}}{\left(2 x - 1\right)^{2} + 1}
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Segunda derivada [src] 
                                                             2          
  /          2                                        \  atan (-1 + 2*x)
8*\1 + 2*atan (-1 + 2*x) - 2*(-1 + 2*x)*atan(-1 + 2*x)/*e               
------------------------------------------------------------------------
                                            2                           
                           /              2\                            
                           \1 + (-1 + 2*x) /
8(−2(2x−1)atan⁡(2x−1)+2atan⁡2(2x−1)+1)eatan⁡2(2x−1)((2x−1)2+1)2\frac{8 \left(- 2 \left(2 x - 1\right) \operatorname{atan}{\left(2 x - 1 \right)} + 2 \operatorname{atan}^{2}{\left(2 x - 1 \right)} + 1\right) e^{\operatorname{atan}^{2}{\left(2 x - 1 \right)}}}{\left(\left(2 x - 1\right)^{2} + 1\right)^{2}}
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Tercera derivada [src] 
   /                                          3                                      2                                    2               \      2          
   |                    3*(-1 + 2*x)    2*atan (-1 + 2*x)   3*atan(-1 + 2*x)   6*atan (-1 + 2*x)*(-1 + 2*x)   4*(-1 + 2*x) *atan(-1 + 2*x)|  atan (-1 + 2*x)
32*|-atan(-1 + 2*x) - --------------- + ----------------- + ---------------- - ---------------------------- + ----------------------------|*e               
   |                                2                  2                  2                        2                              2       |                 
   \                  1 + (-1 + 2*x)     1 + (-1 + 2*x)     1 + (-1 + 2*x)           1 + (-1 + 2*x)                 1 + (-1 + 2*x)        /                 
------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                      2                                                                     
                                                                     /              2\                                                                      
                                                                     \1 + (-1 + 2*x) /
32(4(2x−1)2atan⁡(2x−1)(2x−1)2+1−6(2x−1)atan⁡2(2x−1)(2x−1)2+1−3(2x−1)(2x−1)2+1−atan⁡(2x−1)+2atan⁡3(2x−1)(2x−1)2+1+3atan⁡(2x−1)(2x−1)2+1)eatan⁡2(2x−1)((2x−1)2+1)2\frac{32 \left(\frac{4 \left(2 x - 1\right)^{2} \operatorname{atan}{\left(2 x - 1 \right)}}{\left(2 x - 1\right)^{2} + 1} - \frac{6 \left(2 x - 1\right) \operatorname{atan}^{2}{\left(2 x - 1 \right)}}{\left(2 x - 1\right)^{2} + 1} - \frac{3 \left(2 x - 1\right)}{\left(2 x - 1\right)^{2} + 1} - \operatorname{atan}{\left(2 x - 1 \right)} + \frac{2 \operatorname{atan}^{3}{\left(2 x - 1 \right)}}{\left(2 x - 1\right)^{2} + 1} + \frac{3 \operatorname{atan}{\left(2 x - 1 \right)}}{\left(2 x - 1\right)^{2} + 1}\right) e^{\operatorname{atan}^{2}{\left(2 x - 1 \right)}}}{\left(\left(2 x - 1\right)^{2} + 1\right)^{2}}
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Gráfico
Derivada de y=e^arctg^2(2x-1)
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