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y=1/sqrt(2)arctg(x^2-1)/x*sqrt(2)

  • ¿Cómo usar?

  • Derivada de:
  • Derivada de 2*cos(x)/sin(x) Derivada de 2*cos(x)/sin(x)
  • Derivada de (27/10)*t+(3/4) Derivada de (27/10)*t+(3/4)
  • Derivada de (1+4x^2)^3 Derivada de (1+4x^2)^3
  • Derivada de y(x)=tg5x Derivada de y(x)=tg5x

  • Expresiones idénticas

  • y= uno /sqrt(dos)arctg(x^ dos - uno)/x*sqrt(dos)
  • y es igual a 1 dividir por raíz cuadrada de (2)arctg(x al cuadrado menos 1) dividir por x multiplicar por raíz cuadrada de (2)
  • y es igual a uno dividir por raíz cuadrada de (dos)arctg(x en el grado dos menos uno) dividir por x multiplicar por raíz cuadrada de (dos)
  • y=1/√(2)arctg(x^2-1)/x*√(2)
  • y=1/sqrt(2)arctg(x2-1)/x*sqrt(2)
  • y=1/sqrt2arctgx2-1/x*sqrt2
  • y=1/sqrt(2)arctg(x²-1)/x*sqrt(2)
  • y=1/sqrt(2)arctg(x en el grado 2-1)/x*sqrt(2)
  • y=1/sqrt(2)arctg(x^2-1)/xsqrt(2)
  • y=1/sqrt(2)arctg(x2-1)/xsqrt(2)
  • y=1/sqrt2arctgx2-1/xsqrt2
  • y=1/sqrt2arctgx^2-1/xsqrt2
  • y=1 dividir por sqrt(2)arctg(x^2-1) dividir por x*sqrt(2)

  • Expresiones semejantes

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

Derivada de y=1/sqrt(2)arctg(x^2-1)/x*sqrt(2)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
/    / 2    \\      
|atan\x  - 1/|      
|------------|      
|     ___    |      
\   \/ 2     /   ___
--------------*\/ 2 
      x
212atan⁡(x2−1)x\sqrt{2} \frac{\frac{1}{\sqrt{2}} \operatorname{atan}{\left(x^{2} - 1 \right)}}{x} 
((atan(x^2 - 1)/sqrt(2))/x)*sqrt(2)
Gráfica
02468-8-6-4-2-1010-100100
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
      /                  ___             \
      |                \/ 2      / 2    \|
      |      ___       -----*atan\x  - 1/|
  ___ |    \/ 2          2               |
\/ 2 *|------------- - ------------------|
      |            2            2        |
      |    / 2    \            x         |
      \1 + \x  - 1/                      /
2(2(x2−1)2+1−22atan⁡(x2−1)x2)\sqrt{2} \left(\frac{\sqrt{2}}{\left(x^{2} - 1\right)^{2} + 1} - \frac{\frac{\sqrt{2}}{2} \operatorname{atan}{\left(x^{2} - 1 \right)}}{x^{2}}\right)
Simplificar
Segunda derivada [src] 
   /                         2 /      2\                \
   |                      4*x *\-1 + x /                |
   |                 -1 + --------------                |
   |                                   2                |
   |                          /      2\        /      2\|
   |      2               1 + \-1 + x /    atan\-1 + x /|
-2*|-------------- + ------------------- - -------------|
   |             2                   2            2     |
   |    /      2\           /      2\            x      |
   \1 + \-1 + x /       1 + \-1 + x /                   /
---------------------------------------------------------
                            x
−2(4x2(x2−1)(x2−1)2+1−1(x2−1)2+1+2(x2−1)2+1−atan⁡(x2−1)x2)x- \frac{2 \left(\frac{\frac{4 x^{2} \left(x^{2} - 1\right)}{\left(x^{2} - 1\right)^{2} + 1} - 1}{\left(x^{2} - 1\right)^{2} + 1} + \frac{2}{\left(x^{2} - 1\right)^{2} + 1} - \frac{\operatorname{atan}{\left(x^{2} - 1 \right)}}{x^{2}}\right)}{x}
Simplificar
Tercera derivada [src] 
  /                      /                         2\                                                \
  |                      |              2 /      2\ |                           /        2 /      2\\|
  |                      |       2   8*x *\-1 + x / |                           |     4*x *\-1 + x /||
  |                    4*|3 - 5*x  + ---------------|                         3*|-1 + --------------||
  |                      |                         2|                           |                  2||
  |        /      2\     |                /      2\ |                           |         /      2\ ||
  |  3*atan\-1 + x /     \            1 + \-1 + x / /            6              \     1 + \-1 + x / /|
2*|- --------------- + ------------------------------ + ------------------- + -----------------------|
  |          4                               2             /             2\        /             2\  |
  |         x                /             2\            2 |    /      2\ |      2 |    /      2\ |  |
  |                          |    /      2\ |           x *\1 + \-1 + x / /     x *\1 + \-1 + x / /  |
  \                          \1 + \-1 + x / /                                                        /
2(4(8x2(x2−1)2(x2−1)2+1−5x2+3)((x2−1)2+1)2+3(4x2(x2−1)(x2−1)2+1−1)x2((x2−1)2+1)+6x2((x2−1)2+1)−3atan⁡(x2−1)x4)2 \left(\frac{4 \left(\frac{8 x^{2} \left(x^{2} - 1\right)^{2}}{\left(x^{2} - 1\right)^{2} + 1} - 5 x^{2} + 3\right)}{\left(\left(x^{2} - 1\right)^{2} + 1\right)^{2}} + \frac{3 \left(\frac{4 x^{2} \left(x^{2} - 1\right)}{\left(x^{2} - 1\right)^{2} + 1} - 1\right)}{x^{2} \left(\left(x^{2} - 1\right)^{2} + 1\right)} + \frac{6}{x^{2} \left(\left(x^{2} - 1\right)^{2} + 1\right)} - \frac{3 \operatorname{atan}{\left(x^{2} - 1 \right)}}{x^{4}}\right)
Simplificar
3-я производная [src] 
  /                      /                         2\                                                \
  |                      |              2 /      2\ |                           /        2 /      2\\|
  |                      |       2   8*x *\-1 + x / |                           |     4*x *\-1 + x /||
  |                    4*|3 - 5*x  + ---------------|                         3*|-1 + --------------||
  |                      |                         2|                           |                  2||
  |        /      2\     |                /      2\ |                           |         /      2\ ||
  |  3*atan\-1 + x /     \            1 + \-1 + x / /            6              \     1 + \-1 + x / /|
2*|- --------------- + ------------------------------ + ------------------- + -----------------------|
  |          4                               2             /             2\        /             2\  |
  |         x                /             2\            2 |    /      2\ |      2 |    /      2\ |  |
  |                          |    /      2\ |           x *\1 + \-1 + x / /     x *\1 + \-1 + x / /  |
  \                          \1 + \-1 + x / /                                                        /
2(4(8x2(x2−1)2(x2−1)2+1−5x2+3)((x2−1)2+1)2+3(4x2(x2−1)(x2−1)2+1−1)x2((x2−1)2+1)+6x2((x2−1)2+1)−3atan⁡(x2−1)x4)2 \left(\frac{4 \left(\frac{8 x^{2} \left(x^{2} - 1\right)^{2}}{\left(x^{2} - 1\right)^{2} + 1} - 5 x^{2} + 3\right)}{\left(\left(x^{2} - 1\right)^{2} + 1\right)^{2}} + \frac{3 \left(\frac{4 x^{2} \left(x^{2} - 1\right)}{\left(x^{2} - 1\right)^{2} + 1} - 1\right)}{x^{2} \left(\left(x^{2} - 1\right)^{2} + 1\right)} + \frac{6}{x^{2} \left(\left(x^{2} - 1\right)^{2} + 1\right)} - \frac{3 \operatorname{atan}{\left(x^{2} - 1 \right)}}{x^{4}}\right)
Simplificar
Gráfico
Derivada de y=1/sqrt(2)arctg(x^2-1)/x*sqrt(2)
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