Sr Examen

Otras calculadoras

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:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
     2/  _________\
 atan \\/ 2*x - 1 /
E
eatan⁡2(2x−1)e^{\operatorname{atan}^{2}{\left(\sqrt{2 x - 1} \right)}} 
E^(atan(sqrt(2*x - 1))^2)
Gráfica
02468-8-6-4-2-1010010
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                       2/  _________\
    /  _________\  atan \\/ 2*x - 1 /
atan\\/ 2*x - 1 /*e                  
-------------------------------------
                _________            
            x*\/ 2*x - 1
eatan⁡2(2x−1)atan⁡(2x−1)x2x−1\frac{e^{\operatorname{atan}^{2}{\left(\sqrt{2 x - 1} \right)}} \operatorname{atan}{\left(\sqrt{2 x - 1} \right)}}{x \sqrt{2 x - 1}}
Simplificar
Segunda derivada [src] 
/                     /  __________\       2/  __________\       /  __________\\      2/  __________\
|      1          atan\\/ -1 + 2*x /   atan \\/ -1 + 2*x /   atan\\/ -1 + 2*x /|  atan \\/ -1 + 2*x /
|-------------- - ------------------ + ------------------- - ------------------|*e                   
|2*x*(-1 + 2*x)               3/2          x*(-1 + 2*x)            __________  |                     
\                   (-1 + 2*x)                                 x*\/ -1 + 2*x   /                     
-----------------------------------------------------------------------------------------------------
                                                  x
(−atan⁡(2x−1)(2x−1)32+atan⁡2(2x−1)x(2x−1)+12x(2x−1)−atan⁡(2x−1)x2x−1)eatan⁡2(2x−1)x\frac{\left(- \frac{\operatorname{atan}{\left(\sqrt{2 x - 1} \right)}}{\left(2 x - 1\right)^{\frac{3}{2}}} + \frac{\operatorname{atan}^{2}{\left(\sqrt{2 x - 1} \right)}}{x \left(2 x - 1\right)} + \frac{1}{2 x \left(2 x - 1\right)} - \frac{\operatorname{atan}{\left(\sqrt{2 x - 1} \right)}}{x \sqrt{2 x - 1}}\right) e^{\operatorname{atan}^{2}{\left(\sqrt{2 x - 1} \right)}}}{x}
Simplificar
Tercera derivada [src] 
/      /  __________\                                           3/  __________\         2/  __________\         2/  __________\         /  __________\         /  __________\         /  __________\\      2/  __________\
|3*atan\\/ -1 + 2*x /          3                 3          atan \\/ -1 + 2*x /   3*atan \\/ -1 + 2*x /   3*atan \\/ -1 + 2*x /   2*atan\\/ -1 + 2*x /   2*atan\\/ -1 + 2*x /   3*atan\\/ -1 + 2*x /|  atan \\/ -1 + 2*x /
|-------------------- - --------------- - --------------- + ------------------- - --------------------- - --------------------- + -------------------- + -------------------- + --------------------|*e                   
|             5/2                     2      2                 2           3/2                    2            2                                3/2         2   __________          2           3/2 |                     
\   (-1 + 2*x)          2*x*(-1 + 2*x)    2*x *(-1 + 2*x)     x *(-1 + 2*x)           x*(-1 + 2*x)            x *(-1 + 2*x)         x*(-1 + 2*x)           x *\/ -1 + 2*x        2*x *(-1 + 2*x)    /                     
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                            x
(3atan⁡(2x−1)(2x−1)52−3atan⁡2(2x−1)x(2x−1)2−32x(2x−1)2+2atan⁡(2x−1)x(2x−1)32−3atan⁡2(2x−1)x2(2x−1)−32x2(2x−1)+2atan⁡(2x−1)x22x−1+atan⁡3(2x−1)x2(2x−1)32+3atan⁡(2x−1)2x2(2x−1)32)eatan⁡2(2x−1)x\frac{\left(\frac{3 \operatorname{atan}{\left(\sqrt{2 x - 1} \right)}}{\left(2 x - 1\right)^{\frac{5}{2}}} - \frac{3 \operatorname{atan}^{2}{\left(\sqrt{2 x - 1} \right)}}{x \left(2 x - 1\right)^{2}} - \frac{3}{2 x \left(2 x - 1\right)^{2}} + \frac{2 \operatorname{atan}{\left(\sqrt{2 x - 1} \right)}}{x \left(2 x - 1\right)^{\frac{3}{2}}} - \frac{3 \operatorname{atan}^{2}{\left(\sqrt{2 x - 1} \right)}}{x^{2} \left(2 x - 1\right)} - \frac{3}{2 x^{2} \left(2 x - 1\right)} + \frac{2 \operatorname{atan}{\left(\sqrt{2 x - 1} \right)}}{x^{2} \sqrt{2 x - 1}} + \frac{\operatorname{atan}^{3}{\left(\sqrt{2 x - 1} \right)}}{x^{2} \left(2 x - 1\right)^{\frac{3}{2}}} + \frac{3 \operatorname{atan}{\left(\sqrt{2 x - 1} \right)}}{2 x^{2} \left(2 x - 1\right)^{\frac{3}{2}}}\right) e^{\operatorname{atan}^{2}{\left(\sqrt{2 x - 1} \right)}}}{x}
Simplificar
Gráfico
Derivada de y=e^arctg^2(√(2x-1))
    © Sr Examen – Калькулятор