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y=e^arctg^2√(2x-1)
Derivada de la función/ ctg^2/ (2x-1)/ arctg/ 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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Definida a trozos:

Solución

Ha introducido [src] 
     2               
 atan (x)   _________
E        *\/ 2*x - 1
eatan⁡2(x)2x−1e^{\operatorname{atan}^{2}{\left(x \right)}} \sqrt{2 x - 1} 
E^(atan(x)^2)*sqrt(2*x - 1)
Gráfica
02468-8-6-4-2-1010050
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Primera derivada [src] 
      2                                  2   
  atan (x)        _________          atan (x)
 e            2*\/ 2*x - 1 *atan(x)*e        
----------- + -------------------------------
  _________                     2            
\/ 2*x - 1                 1 + x
22x−1eatan⁡2(x)atan⁡(x)x2+1+eatan⁡2(x)2x−1\frac{2 \sqrt{2 x - 1} e^{\operatorname{atan}^{2}{\left(x \right)}} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{e^{\operatorname{atan}^{2}{\left(x \right)}}}{\sqrt{2 x - 1}}
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Segunda derivada [src] 
/                      __________ /          2                 \                        \      2   
|        1         2*\/ -1 + 2*x *\1 + 2*atan (x) - 2*x*atan(x)/         4*atan(x)      |  atan (x)
|- ------------- + --------------------------------------------- + ---------------------|*e        
|            3/2                             2                     /     2\   __________|          
|  (-1 + 2*x)                        /     2\                      \1 + x /*\/ -1 + 2*x |          
\                                    \1 + x /                                           /
(22x−1(−2xatan⁡(x)+2atan⁡2(x)+1)(x2+1)2+4atan⁡(x)2x−1(x2+1)−1(2x−1)32)eatan⁡2(x)\left(\frac{2 \sqrt{2 x - 1} \left(- 2 x \operatorname{atan}{\left(x \right)} + 2 \operatorname{atan}^{2}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2}} + \frac{4 \operatorname{atan}{\left(x \right)}}{\sqrt{2 x - 1} \left(x^{2} + 1\right)} - \frac{1}{\left(2 x - 1\right)^{\frac{3}{2}}}\right) e^{\operatorname{atan}^{2}{\left(x \right)}}
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Tercera derivada [src] 
/                                                        /                          3                          2         2        \                                   \          
|                                             __________ |            3*x     2*atan (x)   3*atan(x)   6*x*atan (x)   4*x *atan(x)|                                   |          
|                                         4*\/ -1 + 2*x *|-atan(x) - ------ + ---------- + --------- - ------------ + ------------|                                   |          
|                                                        |                2          2            2            2              2   |     /          2                 \|      2   
|      3               6*atan(x)                         \           1 + x      1 + x        1 + x        1 + x          1 + x    /   6*\1 + 2*atan (x) - 2*x*atan(x)/|  atan (x)
|------------- - ---------------------- + ----------------------------------------------------------------------------------------- + --------------------------------|*e        
|          5/2   /     2\           3/2                                                   2                                                        2                  |          
|(-1 + 2*x)      \1 + x /*(-1 + 2*x)                                              /     2\                                                 /     2\    __________     |          
\                                                                                 \1 + x /                                                 \1 + x / *\/ -1 + 2*x      /
(42x−1(4x2atan⁡(x)x2+1−6xatan⁡2(x)x2+1−3xx2+1−atan⁡(x)+2atan⁡3(x)x2+1+3atan⁡(x)x2+1)(x2+1)2+6(−2xatan⁡(x)+2atan⁡2(x)+1)2x−1(x2+1)2−6atan⁡(x)(2x−1)32(x2+1)+3(2x−1)52)eatan⁡2(x)\left(\frac{4 \sqrt{2 x - 1} \left(\frac{4 x^{2} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \frac{6 x \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{3 x}{x^{2} + 1} - \operatorname{atan}{\left(x \right)} + \frac{2 \operatorname{atan}^{3}{\left(x \right)}}{x^{2} + 1} + \frac{3 \operatorname{atan}{\left(x \right)}}{x^{2} + 1}\right)}{\left(x^{2} + 1\right)^{2}} + \frac{6 \left(- 2 x \operatorname{atan}{\left(x \right)} + 2 \operatorname{atan}^{2}{\left(x \right)} + 1\right)}{\sqrt{2 x - 1} \left(x^{2} + 1\right)^{2}} - \frac{6 \operatorname{atan}{\left(x \right)}}{\left(2 x - 1\right)^{\frac{3}{2}} \left(x^{2} + 1\right)} + \frac{3}{\left(2 x - 1\right)^{\frac{5}{2}}}\right) e^{\operatorname{atan}^{2}{\left(x \right)}}
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Gráfico
Derivada de y=e^arctg^2√(2x-1)
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