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xe^arctg(sqrt2x-1)
Derivada de la función/ arctg/ sqrt2/ xe^arctg(sqrt2x-1)

Derivada de xe^arctg(sqrt2x-1)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
       /  _____    \
   atan\\/ 2*x  - 1/
x*E
eatan⁡(2x−1)xe^{\operatorname{atan}{\left(\sqrt{2 x} - 1 \right)}} x 
x*E^atan(sqrt(2*x) - 1)
Gráfica
02468-8-6-4-2-1010050
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                                      /  _____    \
     /  _____    \     ___   ___  atan\\/ 2*x  - 1/
 atan\\/ 2*x  - 1/   \/ 2 *\/ x *e                 
E                  + ------------------------------
                           /                 2\    
                           |    /  _____    \ |    
                         2*\1 + \\/ 2*x  - 1/ /
eatan⁡(2x−1)+2xeatan⁡(2x−1)2((2x−1)2+1)e^{\operatorname{atan}{\left(\sqrt{2 x} - 1 \right)}} + \frac{\sqrt{2} \sqrt{x} e^{\operatorname{atan}{\left(\sqrt{2 x} - 1 \right)}}}{2 \left(\left(\sqrt{2 x} - 1\right)^{2} + 1\right)}
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Segunda derivada [src] 
/          /  ___                                       /       ___   ___\   \\                        
|          |\/ 2                 2                    4*\-1 + \/ 2 *\/ x /   ||                        
|        x*|----- - --------------------------- + ---------------------------||                        
|          |  3/2     /                      2\     /                      2\||                        
|  ___     | x        |    /       ___   ___\ |     |    /       ___   ___\ |||      /       ___   ___\
|\/ 2      \        x*\1 + \-1 + \/ 2 *\/ x / /   x*\1 + \-1 + \/ 2 *\/ x / //|  atan\-1 + \/ 2 *\/ x /
|----- - ---------------------------------------------------------------------|*e                      
|  ___                                     4                                  |                        
\\/ x                                                                         /                        
-------------------------------------------------------------------------------------------------------
                                                              2                                        
                                            /       ___   ___\                                         
                                        1 + \-1 + \/ 2 *\/ x /
(−x(4(2x−1)x((2x−1)2+1)−2x((2x−1)2+1)+2x32)4+2x)eatan⁡(2x−1)(2x−1)2+1\frac{\left(- \frac{x \left(\frac{4 \left(\sqrt{2} \sqrt{x} - 1\right)}{x \left(\left(\sqrt{2} \sqrt{x} - 1\right)^{2} + 1\right)} - \frac{2}{x \left(\left(\sqrt{2} \sqrt{x} - 1\right)^{2} + 1\right)} + \frac{\sqrt{2}}{x^{\frac{3}{2}}}\right)}{4} + \frac{\sqrt{2}}{\sqrt{x}}\right) e^{\operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}}{\left(\sqrt{2} \sqrt{x} - 1\right)^{2} + 1}
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Tercera derivada [src] 
/              /                                                                                                                                                                                                            2 \                                                              \                        
|              |                                     ___                  ___                               ___                     /       ___   ___\              ___ /       ___   ___\            ___ /       ___   ___\  |                                                              |                        
|              |               6                 3*\/ 2               4*\/ 2                            2*\/ 2                   12*\-1 + \/ 2 *\/ x /         12*\/ 2 *\-1 + \/ 2 *\/ x /       16*\/ 2 *\-1 + \/ 2 *\/ x /  |                                                              |                        
|            x*|- ---------------------------- + ------- - ------------------------------ + ------------------------------- + ---------------------------- - ------------------------------- + -------------------------------|                                                              |                        
|              |     /                      2\      5/2         /                      2\                                 2      /                      2\                                 2                                 2|                                                              |                        
|              |   2 |    /       ___   ___\ |     x        3/2 |    /       ___   ___\ |        /                      2\     2 |    /       ___   ___\ |        /                      2\         /                      2\ |                                                              |                        
|      ___     |  x *\1 + \-1 + \/ 2 *\/ x / /             x   *\1 + \-1 + \/ 2 *\/ x / /    3/2 |    /       ___   ___\ |    x *\1 + \-1 + \/ 2 *\/ x / /    3/2 |    /       ___   ___\ |     3/2 |    /       ___   ___\ | |                                         /       ___   ___\   |      /       ___   ___\
|  3*\/ 2      \                                                                            x   *\1 + \-1 + \/ 2 *\/ x / /                                   x   *\1 + \-1 + \/ 2 *\/ x / /    x   *\1 + \-1 + \/ 2 *\/ x / / /                 3                     3*\-1 + \/ 2 *\/ x /   |  atan\-1 + \/ 2 *\/ x /
|- ------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ----------------------------- - ---------------------------|*e                      
|      3/2                                                                                                           8                                                                                                                /                      2\     /                      2\|                        
|   4*x                                                                                                                                                                                                                               |    /       ___   ___\ |     |    /       ___   ___\ ||                        
\                                                                                                                                                                                                                                 2*x*\1 + \-1 + \/ 2 *\/ x / /   x*\1 + \-1 + \/ 2 *\/ x / //                        
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                     2                                                                                                                                                
                                                                                                                                                   /       ___   ___\                                                                                                                                                 
                                                                                                                                               1 + \-1 + \/ 2 *\/ x /
(x(12(2x−1)x2((2x−1)2+1)−6x2((2x−1)2+1)+162(2x−1)2x32((2x−1)2+1)2−122(2x−1)x32((2x−1)2+1)2−42x32((2x−1)2+1)+22x32((2x−1)2+1)2+32x52)8−3(2x−1)x((2x−1)2+1)+32x((2x−1)2+1)−324x32)eatan⁡(2x−1)(2x−1)2+1\frac{\left(\frac{x \left(\frac{12 \left(\sqrt{2} \sqrt{x} - 1\right)}{x^{2} \left(\left(\sqrt{2} \sqrt{x} - 1\right)^{2} + 1\right)} - \frac{6}{x^{2} \left(\left(\sqrt{2} \sqrt{x} - 1\right)^{2} + 1\right)} + \frac{16 \sqrt{2} \left(\sqrt{2} \sqrt{x} - 1\right)^{2}}{x^{\frac{3}{2}} \left(\left(\sqrt{2} \sqrt{x} - 1\right)^{2} + 1\right)^{2}} - \frac{12 \sqrt{2} \left(\sqrt{2} \sqrt{x} - 1\right)}{x^{\frac{3}{2}} \left(\left(\sqrt{2} \sqrt{x} - 1\right)^{2} + 1\right)^{2}} - \frac{4 \sqrt{2}}{x^{\frac{3}{2}} \left(\left(\sqrt{2} \sqrt{x} - 1\right)^{2} + 1\right)} + \frac{2 \sqrt{2}}{x^{\frac{3}{2}} \left(\left(\sqrt{2} \sqrt{x} - 1\right)^{2} + 1\right)^{2}} + \frac{3 \sqrt{2}}{x^{\frac{5}{2}}}\right)}{8} - \frac{3 \left(\sqrt{2} \sqrt{x} - 1\right)}{x \left(\left(\sqrt{2} \sqrt{x} - 1\right)^{2} + 1\right)} + \frac{3}{2 x \left(\left(\sqrt{2} \sqrt{x} - 1\right)^{2} + 1\right)} - \frac{3 \sqrt{2}}{4 x^{\frac{3}{2}}}\right) e^{\operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}}{\left(\sqrt{2} \sqrt{x} - 1\right)^{2} + 1}
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Gráfico
Derivada de xe^arctg(sqrt2x-1)
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