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y=x^((e^(arctg(x))/(x^2+1)))

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  • Derivada de:
  • Derivada de e^x*sin(x) Derivada de e^x*sin(x)
  • Derivada de 5^10 Derivada de 5^10
  • Derivada de 2*cos(3*x) Derivada de 2*cos(3*x)
  • Derivada de 1/t Derivada de 1/t

  • Expresiones idénticas

  • y=x^((e^(arctg(x))/(x^ dos + uno)))
  • y es igual a x en el grado ((e en el grado (arctg(x)) dividir por (x al cuadrado más 1)))
  • y es igual a x en el grado ((e en el grado (arctg(x)) dividir por (x en el grado dos más uno)))
  • y=x((e(arctg(x))/(x2+1)))
  • y=xearctgx/x2+1
  • y=x^((e^(arctg(x))/(x²+1)))
  • y=x en el grado ((e en el grado (arctg(x))/(x en el grado 2+1)))
  • y=x^e^arctgx/x^2+1
  • y=x^((e^(arctg(x)) dividir por (x^2+1)))

  • Expresiones semejantes

  • y=x^((e^(arctg(x))/(x^2-1)))

  • Expresiones con funciones

  • arctg
  • arctg^2(1/x)
Derivada de la función/ y=x^((e^(arctg(x))/(x^2+1)))

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

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  atan(x)
 E       
 --------
   2     
  x  + 1 
x
xeatan⁡(x)x2+1x^{\frac{e^{\operatorname{atan}{\left(x \right)}}}{x^{2} + 1}} 
x^(E^atan(x)/(x^2 + 1))
Solución detallada

  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (eatan⁡(x)x2+1)eatan⁡(x)x2+1(log⁡(eatan⁡(x)x2+1)+1)\left(\frac{e^{\operatorname{atan}{\left(x \right)}}}{x^{2} + 1}\right)^{\frac{e^{\operatorname{atan}{\left(x \right)}}}{x^{2} + 1}} \left(\log{\left(\frac{e^{\operatorname{atan}{\left(x \right)}}}{x^{2} + 1} \right)} + 1\right)

  2. Simplificamos:

    (x2+1)−eatan⁡(x)x2+1(−log⁡(x2+1)+atan⁡(x)+1)eeatan⁡(x)atan⁡(x)x2+1\left(x^{2} + 1\right)^{- \frac{e^{\operatorname{atan}{\left(x \right)}}}{x^{2} + 1}} \left(- \log{\left(x^{2} + 1 \right)} + \operatorname{atan}{\left(x \right)} + 1\right) e^{\frac{e^{\operatorname{atan}{\left(x \right)}} \operatorname{atan}{\left(x \right)}}{x^{2} + 1}}

Respuesta:

(x2+1)−eatan⁡(x)x2+1(−log⁡(x2+1)+atan⁡(x)+1)eeatan⁡(x)atan⁡(x)x2+1\left(x^{2} + 1\right)^{- \frac{e^{\operatorname{atan}{\left(x \right)}}}{x^{2} + 1}} \left(- \log{\left(x^{2} + 1 \right)} + \operatorname{atan}{\left(x \right)} + 1\right) e^{\frac{e^{\operatorname{atan}{\left(x \right)}} \operatorname{atan}{\left(x \right)}}{x^{2} + 1}}

Gráfica
02468-8-6-4-2-10102-2
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
  atan(x)                                                         
 E                                                                
 --------                                                         
   2      //      atan(x)            atan(x)\            atan(x) \
  x  + 1  ||     e              2*x*e       |           e        |
x        *||----------------- - ------------|*log(x) + ----------|
          ||/     2\ / 2    \            2  |            / 2    \|
          ||\1 + x /*\x  + 1/    / 2    \   |          x*\x  + 1/|
          \\                     \x  + 1/   /                    /
xeatan⁡(x)x2+1((−2xeatan⁡(x)(x2+1)2+eatan⁡(x)(x2+1)(x2+1))log⁡(x)+eatan⁡(x)x(x2+1))x^{\frac{e^{\operatorname{atan}{\left(x \right)}}}{x^{2} + 1}} \left(\left(- \frac{2 x e^{\operatorname{atan}{\left(x \right)}}}{\left(x^{2} + 1\right)^{2}} + \frac{e^{\operatorname{atan}{\left(x \right)}}}{\left(x^{2} + 1\right) \left(x^{2} + 1\right)}\right) \log{\left(x \right)} + \frac{e^{\operatorname{atan}{\left(x \right)}}}{x \left(x^{2} + 1\right)}\right)
Simplificar
Segunda derivada [src] 
  atan(x) /                                                      2                         /                 2          \       \         
 e        |                             /  1   (-1 + 2*x)*log(x)\   atan(x)                |      1       8*x      6*x  |       |         
 -------- |                             |- - + -----------------| *e                       |2 - ------ - ------ + ------|*log(x)|         
       2  |                             |  x              2     |                          |         2        2        2|       |         
  1 + x   |  1      2          1        \            1 + x      /              -1 + 2*x    \    1 + x    1 + x    1 + x /       |  atan(x)
x        *|- -- - ------ + ---------- + ----------------------------------- - ---------- - -------------------------------------|*e       
          |   2        2     /     2\                       2                   /     2\                        2               |         
          \  x    1 + x    x*\1 + x /                  1 + x                  x*\1 + x /                   1 + x                /         
------------------------------------------------------------------------------------------------------------------------------------------
                                                                       2                                                                  
                                                                  1 + x
xeatan⁡(x)x2+1(((2x−1)log⁡(x)x2+1−1x)2eatan⁡(x)x2+1−(−8x2x2+1+6xx2+1+2−1x2+1)log⁡(x)x2+1−2x2+1−2x−1x(x2+1)+1x(x2+1)−1x2)eatan⁡(x)x2+1\frac{x^{\frac{e^{\operatorname{atan}{\left(x \right)}}}{x^{2} + 1}} \left(\frac{\left(\frac{\left(2 x - 1\right) \log{\left(x \right)}}{x^{2} + 1} - \frac{1}{x}\right)^{2} e^{\operatorname{atan}{\left(x \right)}}}{x^{2} + 1} - \frac{\left(- \frac{8 x^{2}}{x^{2} + 1} + \frac{6 x}{x^{2} + 1} + 2 - \frac{1}{x^{2} + 1}\right) \log{\left(x \right)}}{x^{2} + 1} - \frac{2}{x^{2} + 1} - \frac{2 x - 1}{x \left(x^{2} + 1\right)} + \frac{1}{x \left(x^{2} + 1\right)} - \frac{1}{x^{2}}\right) e^{\operatorname{atan}{\left(x \right)}}}{x^{2} + 1}
Simplificar
Tercera derivada [src] 
          /                                                                                                                                                                                                                                                     /                                        /                 2          \       \         \         
          |                                                                                                                                                                                                                                                     |                                        |      1       8*x      6*x  |       |         |         
          |                                                                                                                                                                                                                                                     |                                        |2 - ------ - ------ + ------|*log(x)|         |         
  atan(x) |                                                                                                               3              /                        2                 3 \            /                 2          \                               |                                        |         2        2        2|       |         |         
 e        |                                                                                      /  1   (-1 + 2*x)*log(x)\   2*atan(x)   |      1             44*x      12*x    48*x  |            |      1       8*x      6*x  |     /  1   (-1 + 2*x)*log(x)\ |1      2          1         -1 + 2*x    \    1 + x    1 + x    1 + x /       |  atan(x)|         
 -------- |                                                                                      |- - + -----------------| *e            |8 - ------ - 24*x - ------ + ------ + ------|*log(x)   2*|2 - ------ - ------ + ------|   3*|- - + -----------------|*|-- + ------ - ---------- + ---------- + -------------------------------------|*e       |         
       2  |                                                                                      |  x              2     |               |         2               2        2        2|            |         2        2        2|     |  x              2     | | 2        2     /     2\     /     2\                        2               |         |         
  1 + x   |      6       2         1             2            2           8*x        -1 + 2*x    \            1 + x      /               \    1 + x           1 + x    1 + x    1 + x /            \    1 + x    1 + x    1 + x /     \            1 + x      / \x    1 + x    x*\1 + x /   x*\1 + x /                   1 + x                /         |  atan(x)
x        *|- --------- + -- + ----------- - ----------- + ---------- + --------- + ----------- - ------------------------------------- - ----------------------------------------------------- - -------------------------------- + --------------------------------------------------------------------------------------------------------------------|*e       
          |          2    3             2    2 /     2\     /     2\           2    2 /     2\                         2                                               2                                      /     2\                                                                          2                                                       |         
          |  /     2\    x      /     2\    x *\1 + x /   x*\1 + x /   /     2\    x *\1 + x /                 /     2\                                        /     2\                                     x*\1 + x /                                                                     1 + x                                                        |         
          \  \1 + x /         x*\1 + x /                               \1 + x /                                \1 + x /                                        \1 + x /                                                                                                                                                                                 /         
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                   2                                                                                                                                                                              
                                                                                                                                                                              1 + x
xeatan⁡(x)x2+1(8x(x2+1)2+3((2x−1)log⁡(x)x2+1−1x)((−8x2x2+1+6xx2+1+2−1x2+1)log⁡(x)x2+1+2x2+1+2x−1x(x2+1)−1x(x2+1)+1x2)eatan⁡(x)x2+1−((2x−1)log⁡(x)x2+1−1x)3e2atan⁡(x)(x2+1)2−(48x3x2+1−44x2x2+1−24x+12xx2+1+8−1x2+1)log⁡(x)(x2+1)2−6(x2+1)2−2(−8x2x2+1+6xx2+1+2−1x2+1)x(x2+1)+2x(x2+1)+1x(x2+1)2+2x−1x2(x2+1)−2x2(x2+1)+2x3)eatan⁡(x)x2+1\frac{x^{\frac{e^{\operatorname{atan}{\left(x \right)}}}{x^{2} + 1}} \left(\frac{8 x}{\left(x^{2} + 1\right)^{2}} + \frac{3 \left(\frac{\left(2 x - 1\right) \log{\left(x \right)}}{x^{2} + 1} - \frac{1}{x}\right) \left(\frac{\left(- \frac{8 x^{2}}{x^{2} + 1} + \frac{6 x}{x^{2} + 1} + 2 - \frac{1}{x^{2} + 1}\right) \log{\left(x \right)}}{x^{2} + 1} + \frac{2}{x^{2} + 1} + \frac{2 x - 1}{x \left(x^{2} + 1\right)} - \frac{1}{x \left(x^{2} + 1\right)} + \frac{1}{x^{2}}\right) e^{\operatorname{atan}{\left(x \right)}}}{x^{2} + 1} - \frac{\left(\frac{\left(2 x - 1\right) \log{\left(x \right)}}{x^{2} + 1} - \frac{1}{x}\right)^{3} e^{2 \operatorname{atan}{\left(x \right)}}}{\left(x^{2} + 1\right)^{2}} - \frac{\left(\frac{48 x^{3}}{x^{2} + 1} - \frac{44 x^{2}}{x^{2} + 1} - 24 x + \frac{12 x}{x^{2} + 1} + 8 - \frac{1}{x^{2} + 1}\right) \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{6}{\left(x^{2} + 1\right)^{2}} - \frac{2 \left(- \frac{8 x^{2}}{x^{2} + 1} + \frac{6 x}{x^{2} + 1} + 2 - \frac{1}{x^{2} + 1}\right)}{x \left(x^{2} + 1\right)} + \frac{2}{x \left(x^{2} + 1\right)} + \frac{1}{x \left(x^{2} + 1\right)^{2}} + \frac{2 x - 1}{x^{2} \left(x^{2} + 1\right)} - \frac{2}{x^{2} \left(x^{2} + 1\right)} + \frac{2}{x^{3}}\right) e^{\operatorname{atan}{\left(x \right)}}}{x^{2} + 1}
Simplificar
Gráfico
Derivada de y=x^((e^(arctg(x))/(x^2+1)))
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