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x×sqrt(1-x²)/(1+x²)-3/sqrt(2)×arctg(xsqrt(2)/sqrt(1-x²))
Derivada de la función/ x×sqrt(1-x²)/(1+x²)-3/sqrt(2)×arctg(xsqrt(2)/sqrt(1-x²))

Derivada de x×sqrt(1-x²)/(1+x²)-3/sqrt(2)×arctg(xsqrt(2)/sqrt(1-x²))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
     ________                          
    /      2              /      ___  \
x*\/  1 - x       3       |  x*\/ 2   |
------------- - -----*atan|-----------|
         2        ___     |   ________|
    1 + x       \/ 2      |  /      2 |
                          \\/  1 - x  /
x1−x2x2+1−32atan⁡(2x1−x2)\frac{x \sqrt{1 - x^{2}}}{x^{2} + 1} - \frac{3}{\sqrt{2}} \operatorname{atan}{\left(\frac{\sqrt{2} x}{\sqrt{1 - x^{2}}} \right)} 
(x*sqrt(1 - x^2))/(1 + x^2) - 3/sqrt(2)*atan((x*sqrt(2))/sqrt(1 - x^2))
Gráfica
02468-8-6-4-2-1010-1010
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
   ________         2                                  /     ___          ___  2 \
  /      2         x                               ___ |   \/ 2         \/ 2 *x  |
\/  1 - x   - -----------                      3*\/ 2 *|----------- + -----------|
                 ________           ________           |   ________           3/2|
                /      2       2   /      2            |  /      2    /     2\   |
              \/  1 - x     2*x *\/  1 - x             \\/  1 - x     \1 - x /   /
------------------------- - ---------------- - -----------------------------------
               2                       2                    /        2 \          
          1 + x                /     2\                     |     2*x  |          
                               \1 + x /                   2*|1 + ------|          
                                                            |         2|          
                                                            \    1 - x /
−2x21−x2(x2+1)2−32(2x2(1−x2)32+21−x2)2(2x21−x2+1)+−x21−x2+1−x2x2+1- \frac{2 x^{2} \sqrt{1 - x^{2}}}{\left(x^{2} + 1\right)^{2}} - \frac{3 \sqrt{2} \left(\frac{\sqrt{2} x^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{\sqrt{2}}{\sqrt{1 - x^{2}}}\right)}{2 \left(\frac{2 x^{2}}{1 - x^{2}} + 1\right)} + \frac{- \frac{x^{2}}{\sqrt{1 - x^{2}}} + \sqrt{1 - x^{2}}}{x^{2} + 1}
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Segunda derivada [src] 
  /                    /     ________         2    \                                                                                                                                       \
  |                    |    /      2         x     |               2                                                             /       2  \                /       2  \ /         2  \   |
  |                  2*|- \/  1 - x   + -----------|              x                                                              |      x   |                |      x   | |        x   |   |
  |       ________     |                   ________|        3 + ------                                        ________         9*|1 + ------|             12*|1 + ------|*|-1 + -------|   |
  |      /      2      |                  /      2 |                 2                    2              2   /      2            |         2|                |         2| |           2|   |
  |  4*\/  1 - x       \                \/  1 - x  /            1 - x                  2*x            8*x *\/  1 - x             \    1 - x /                \    1 - x / \     -1 + x /   |
x*|- ------------- + ------------------------------- - -------------------- + --------------------- + ---------------- + -------------------------- + -------------------------------------|
  |            2                        2                          ________           2    ________              3               3/2 /          2 \                                       2|
  |    /     2\                 /     2\               /     2\   /      2    /     2\    /      2       /     2\        /     2\    |       2*x  |      ________           /          2 \ |
  |    \1 + x /                 \1 + x /               \1 + x /*\/  1 - x     \1 + x / *\/  1 - x        \1 + x /        \1 - x /   *|-1 + -------|     /      2  /      2\ |       2*x  | |
  |                                                                                                                                  |           2|   \/  1 - x  *\-1 + x /*|-1 + -------| |
  |                                                                                                                                  \     -1 + x /                         |           2| |
  \                                                                                                                                                                         \     -1 + x / /
x(8x21−x2(x2+1)3+2x21−x2(x2+1)2−41−x2(x2+1)2+2(x21−x2−1−x2)(x2+1)2−x21−x2+31−x2(x2+1)+12(x21−x2+1)(x2x2−1−1)1−x2(x2−1)(2x2x2−1−1)2+9(x21−x2+1)(1−x2)32(2x2x2−1−1))x \left(\frac{8 x^{2} \sqrt{1 - x^{2}}}{\left(x^{2} + 1\right)^{3}} + \frac{2 x^{2}}{\sqrt{1 - x^{2}} \left(x^{2} + 1\right)^{2}} - \frac{4 \sqrt{1 - x^{2}}}{\left(x^{2} + 1\right)^{2}} + \frac{2 \left(\frac{x^{2}}{\sqrt{1 - x^{2}}} - \sqrt{1 - x^{2}}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{\frac{x^{2}}{1 - x^{2}} + 3}{\sqrt{1 - x^{2}} \left(x^{2} + 1\right)} + \frac{12 \left(\frac{x^{2}}{1 - x^{2}} + 1\right) \left(\frac{x^{2}}{x^{2} - 1} - 1\right)}{\sqrt{1 - x^{2}} \left(x^{2} - 1\right) \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right)^{2}} + \frac{9 \left(\frac{x^{2}}{1 - x^{2}} + 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right)}\right)
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Tercera derivada [src] 
                    /     ________         2    \                                                    /     ________         2    \     /         4          2 \                             /          4         2 \                                                                          /       2  \ /         2          4   \                                                                 2               
                    |    /      2         x     |                                                  2 |    /      2         x     |     |        x        2*x  |                             |       5*x       6*x  |                                                      /       2  \        |      x   | |      5*x        4*x    |           /       2  \ /         2  \             /         2  \  /       2  \  
                  2*|- \/  1 - x   + -----------|                                               8*x *|- \/  1 - x   + -----------|   3*|1 + --------- + ------|                           9*|1 + --------- + ------|                                                    2 |      x   |     12*|1 + ------|*|1 - ------- + ----------|         2 |      x   | |        x   |           2 |        x   |  |      x   |  
       ________     |                   ________|            ________                                |                   ________|     |            2        2|                             |            2        2|                                    ________     4*x *|3 + ------|        |         2| |          2            2|     72*x *|1 + ------|*|-1 + -------|       96*x *|-1 + -------| *|1 + ------|  
      /      2      |                  /      2 |       4   /      2                4                |                  /      2 |     |    /     2\    1 - x |               4             |    /     2\    1 - x |               2               2   /      2           |         2|        \    1 - x / |    -1 + x    /      2\ |           |         2| |           2|             |           2|  |         2|  
  4*\/  1 - x       \                \/  1 - x  /   48*x *\/  1 - x             16*x                 \                \/  1 - x  /     \    \1 - x /          /            2*x              \    \1 - x /          /           10*x            40*x *\/  1 - x            \    1 - x /                     \              \-1 + x / /           \    1 - x / \     -1 + x /             \     -1 + x /  \    1 - x /  
- ------------- + ------------------------------- - ----------------- - --------------------- - ---------------------------------- - -------------------------- + --------------------- + -------------------------- + --------------------- + ----------------- + --------------------- - ------------------------------------------ + ------------------------------------- + --------------------------------------
            2                        2                          4               3    ________                       3                               ________              2         3/2           3/2 /          2 \           2    ________               3               2    ________                                         2                                          2                                        3
    /     2\                 /     2\                   /     2\        /     2\    /      2                /     2\                    /     2\   /      2       /     2\  /     2\      /     2\    |       2*x  |   /     2\    /      2        /     2\        /     2\    /      2         ________           /          2 \               3/2           /          2 \       ________          2 /          2 \ 
    \1 + x /                 \1 + x /                   \1 + x /        \1 + x / *\/  1 - x                 \1 + x /                    \1 + x /*\/  1 - x        \1 + x / *\1 - x /      \1 - x /   *|-1 + -------|   \1 + x / *\/  1 - x         \1 + x /        \1 + x / *\/  1 - x         /      2  /      2\ |       2*x  |       /     2\    /      2\ |       2*x  |      /      2  /      2\  |       2*x  | 
                                                                                                                                                                                                      |           2|                                                                         \/  1 - x  *\-1 + x /*|-1 + -------|       \1 - x /   *\-1 + x /*|-1 + -------|    \/  1 - x  *\-1 + x / *|-1 + -------| 
                                                                                                                                                                                                      \     -1 + x /                                                                                               |           2|                             |           2|                           |           2| 
                                                                                                                                                                                                                                                                                                                   \     -1 + x /                             \     -1 + x /                           \     -1 + x /
−48x41−x2(x2+1)4−16x41−x2(x2+1)3+2x4(1−x2)32(x2+1)2+40x21−x2(x2+1)3−8x2(x21−x2−1−x2)(x2+1)3+4x2(x21−x2+3)1−x2(x2+1)2+10x21−x2(x2+1)2+96x2(x21−x2+1)(x2x2−1−1)21−x2(x2−1)2(2x2x2−1−1)3+72x2(x21−x2+1)(x2x2−1−1)(1−x2)32(x2−1)(2x2x2−1−1)2−41−x2(x2+1)2+2(x21−x2−1−x2)(x2+1)2−3(x4(1−x2)2+2x21−x2+1)1−x2(x2+1)−12(x21−x2+1)(4x4(x2−1)2−5x2x2−1+1)1−x2(x2−1)(2x2x2−1−1)2+9(5x4(1−x2)2+6x21−x2+1)(1−x2)32(2x2x2−1−1)- \frac{48 x^{4} \sqrt{1 - x^{2}}}{\left(x^{2} + 1\right)^{4}} - \frac{16 x^{4}}{\sqrt{1 - x^{2}} \left(x^{2} + 1\right)^{3}} + \frac{2 x^{4}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(x^{2} + 1\right)^{2}} + \frac{40 x^{2} \sqrt{1 - x^{2}}}{\left(x^{2} + 1\right)^{3}} - \frac{8 x^{2} \left(\frac{x^{2}}{\sqrt{1 - x^{2}}} - \sqrt{1 - x^{2}}\right)}{\left(x^{2} + 1\right)^{3}} + \frac{4 x^{2} \left(\frac{x^{2}}{1 - x^{2}} + 3\right)}{\sqrt{1 - x^{2}} \left(x^{2} + 1\right)^{2}} + \frac{10 x^{2}}{\sqrt{1 - x^{2}} \left(x^{2} + 1\right)^{2}} + \frac{96 x^{2} \left(\frac{x^{2}}{1 - x^{2}} + 1\right) \left(\frac{x^{2}}{x^{2} - 1} - 1\right)^{2}}{\sqrt{1 - x^{2}} \left(x^{2} - 1\right)^{2} \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right)^{3}} + \frac{72 x^{2} \left(\frac{x^{2}}{1 - x^{2}} + 1\right) \left(\frac{x^{2}}{x^{2} - 1} - 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(x^{2} - 1\right) \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right)^{2}} - \frac{4 \sqrt{1 - x^{2}}}{\left(x^{2} + 1\right)^{2}} + \frac{2 \left(\frac{x^{2}}{\sqrt{1 - x^{2}}} - \sqrt{1 - x^{2}}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{3 \left(\frac{x^{4}}{\left(1 - x^{2}\right)^{2}} + \frac{2 x^{2}}{1 - x^{2}} + 1\right)}{\sqrt{1 - x^{2}} \left(x^{2} + 1\right)} - \frac{12 \left(\frac{x^{2}}{1 - x^{2}} + 1\right) \left(\frac{4 x^{4}}{\left(x^{2} - 1\right)^{2}} - \frac{5 x^{2}}{x^{2} - 1} + 1\right)}{\sqrt{1 - x^{2}} \left(x^{2} - 1\right) \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right)^{2}} + \frac{9 \left(\frac{5 x^{4}}{\left(1 - x^{2}\right)^{2}} + \frac{6 x^{2}}{1 - x^{2}} + 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right)}
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Gráfico
Derivada de x×sqrt(1-x²)/(1+x²)-3/sqrt(2)×arctg(xsqrt(2)/sqrt(1-x²))
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