Sr Examen

Otras calculadoras

x*sqr(1-x^2)+arctg(x/sqr(1-x^2))
Derivada de la función/ x*sqr(1-x^2)+arctg(x/sqr(1-x^2))

Derivada de x*sqr(1-x^2)+arctg(x/sqr(1-x^2))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  /     2\       2/    x    \
x*\1 - x / + atan |---------|
                  |        2|
                  |/     2\ |
                  \\1 - x / /
x(1−x2)+atan⁡2(x(1−x2)2)x \left(1 - x^{2}\right) + \operatorname{atan}^{2}{\left(\frac{x}{\left(1 - x^{2}\right)^{2}} \right)} 
x*(1 - x^2) + atan(x/(1 - x^2)^2)^2
Gráfica
02468-8-6-4-2-1010-20002000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
             /                  2  \                
             |    1          4*x   |     /    x    \
           2*|--------- + ---------|*atan|---------|
             |        2           3|     |        2|
             |/     2\    /     2\ |     |/     2\ |
       2     \\1 - x /    \1 - x / /     \\1 - x / /
1 - 3*x  + -----------------------------------------
                                  2                 
                                 x                  
                         1 + ---------              
                                     4              
                             /     2\               
                             \1 - x /
−3x2+1+2(4x2(1−x2)3+1(1−x2)2)atan⁡(x(1−x2)2)x2(1−x2)4+1- 3 x^{2} + 1 + \frac{2 \left(\frac{4 x^{2}}{\left(1 - x^{2}\right)^{3}} + \frac{1}{\left(1 - x^{2}\right)^{2}}\right) \operatorname{atan}{\left(\frac{x}{\left(1 - x^{2}\right)^{2}} \right)}}{\frac{x^{2}}{\left(1 - x^{2}\right)^{4}} + 1}
Simplificar
Segunda derivada [src] 
  /                                                        2                                                        \
  |                           2              /          2 \                          /          2 \                 |
  |             /          2 \               |       4*x  |      /    x     \        |       2*x  |     /    x     \|
  |             |       4*x  |           2*x*|-1 + -------| *atan|----------|   12*x*|-1 + -------|*atan|----------||
  |             |-1 + -------|               |           2|      |         2|        |           2|     |         2||
  |             |           2|               \     -1 + x /      |/      2\ |        \     -1 + x /     |/      2\ ||
  |             \     -1 + x /                                   \\-1 + x / /                           \\-1 + x / /|
2*|-3*x + ---------------------------- - ------------------------------------ + ------------------------------------|
  |                       2                                  2                      /         2    \          3     |
  |       /         2    \           4       /         2    \           6           |        x     | /      2\      |
  |       |        x     |  /      2\        |        x     |  /      2\            |1 + ----------|*\-1 + x /      |
  |       |1 + ----------| *\-1 + x /        |1 + ----------| *\-1 + x /            |             4|                |
  |       |             4|                   |             4|                       |    /      2\ |                |
  |       |    /      2\ |                   |    /      2\ |                       \    \-1 + x / /                |
  \       \    \-1 + x / /                   \    \-1 + x / /                                                       /
2(−3x+12x(2x2x2−1−1)atan⁡(x(x2−1)2)(x2−1)3(x2(x2−1)4+1)−2x(4x2x2−1−1)2atan⁡(x(x2−1)2)(x2−1)6(x2(x2−1)4+1)2+(4x2x2−1−1)2(x2−1)4(x2(x2−1)4+1)2)2 \left(- 3 x + \frac{12 x \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right) \operatorname{atan}{\left(\frac{x}{\left(x^{2} - 1\right)^{2}} \right)}}{\left(x^{2} - 1\right)^{3} \left(\frac{x^{2}}{\left(x^{2} - 1\right)^{4}} + 1\right)} - \frac{2 x \left(\frac{4 x^{2}}{x^{2} - 1} - 1\right)^{2} \operatorname{atan}{\left(\frac{x}{\left(x^{2} - 1\right)^{2}} \right)}}{\left(x^{2} - 1\right)^{6} \left(\frac{x^{2}}{\left(x^{2} - 1\right)^{4}} + 1\right)^{2}} + \frac{\left(\frac{4 x^{2}}{x^{2} - 1} - 1\right)^{2}}{\left(x^{2} - 1\right)^{4} \left(\frac{x^{2}}{\left(x^{2} - 1\right)^{4}} + 1\right)^{2}}\right)
Simplificar
Tercera derivada [src] 
  /                                                                                                                                             3                                                                                                                                       \
  |        /         2          4   \                                          3                                                  /          2 \                       /          2 \ /         2          4   \                          /          2 \ /          2 \                 |
  |        |     12*x       16*x    |     /    x     \           /          2 \              /          2 \ /          2 \      2 |       4*x  |      /    x     \     |       4*x  | |     20*x       40*x    |     /    x     \       2 |       2*x  | |       4*x  |     /    x     \|
  |     12*|1 - ------- + ----------|*atan|----------|           |       4*x  |              |       2*x  | |       4*x  |   8*x *|-1 + -------| *atan|----------|   2*|-1 + -------|*|1 - ------- + ----------|*atan|----------|   48*x *|-1 + -------|*|-1 + -------|*atan|----------||
  |        |          2            2|     |         2|       6*x*|-1 + -------|         36*x*|-1 + -------|*|-1 + -------|        |           2|      |         2|     |           2| |          2            2|     |         2|         |           2| |           2|     |         2||
  |        |    -1 + x    /      2\ |     |/      2\ |           |           2|              |           2| |           2|        \     -1 + x /      |/      2\ |     \     -1 + x / |    -1 + x    /      2\ |     |/      2\ |         \     -1 + x / \     -1 + x /     |/      2\ ||
  |        \              \-1 + x / /     \\-1 + x / /           \     -1 + x /              \     -1 + x / \     -1 + x /                            \\-1 + x / /                    \              \-1 + x / /     \\-1 + x / /                                           \\-1 + x / /|
2*|-3 - ---------------------------------------------- + ---------------------------- - ---------------------------------- - ------------------------------------- + ------------------------------------------------------------ + ----------------------------------------------------|
  |              /         2    \          3                             3                                 2                                     3                                                   2                                                          2                       |
  |              |        x     | /      2\              /         2    \           8      /         2    \           5          /         2    \           10                       /         2    \           6                               /         2    \           7            |
  |              |1 + ----------|*\-1 + x /              |        x     |  /      2\       |        x     |  /      2\           |        x     |  /      2\                         |        x     |  /      2\                                |        x     |  /      2\             |
  |              |             4|                        |1 + ----------| *\-1 + x /       |1 + ----------| *\-1 + x /           |1 + ----------| *\-1 + x /                         |1 + ----------| *\-1 + x /                                |1 + ----------| *\-1 + x /             |
  |              |    /      2\ |                        |             4|                  |             4|                      |             4|                                    |             4|                                           |             4|                        |
  |              \    \-1 + x / /                        |    /      2\ |                  |    /      2\ |                      |    /      2\ |                                    |    /      2\ |                                           |    /      2\ |                        |
  \                                                      \    \-1 + x / /                  \    \-1 + x / /                      \    \-1 + x / /                                    \    \-1 + x / /                                           \    \-1 + x / /                        /
2(48x2(2x2x2−1−1)(4x2x2−1−1)atan⁡(x(x2−1)2)(x2−1)7(x2(x2−1)4+1)2−8x2(4x2x2−1−1)3atan⁡(x(x2−1)2)(x2−1)10(x2(x2−1)4+1)3−36x(2x2x2−1−1)(4x2x2−1−1)(x2−1)5(x2(x2−1)4+1)2+6x(4x2x2−1−1)3(x2−1)8(x2(x2−1)4+1)3−3−12(16x4(x2−1)2−12x2x2−1+1)atan⁡(x(x2−1)2)(x2−1)3(x2(x2−1)4+1)+2(4x2x2−1−1)(40x4(x2−1)2−20x2x2−1+1)atan⁡(x(x2−1)2)(x2−1)6(x2(x2−1)4+1)2)2 \left(\frac{48 x^{2} \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right) \left(\frac{4 x^{2}}{x^{2} - 1} - 1\right) \operatorname{atan}{\left(\frac{x}{\left(x^{2} - 1\right)^{2}} \right)}}{\left(x^{2} - 1\right)^{7} \left(\frac{x^{2}}{\left(x^{2} - 1\right)^{4}} + 1\right)^{2}} - \frac{8 x^{2} \left(\frac{4 x^{2}}{x^{2} - 1} - 1\right)^{3} \operatorname{atan}{\left(\frac{x}{\left(x^{2} - 1\right)^{2}} \right)}}{\left(x^{2} - 1\right)^{10} \left(\frac{x^{2}}{\left(x^{2} - 1\right)^{4}} + 1\right)^{3}} - \frac{36 x \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right) \left(\frac{4 x^{2}}{x^{2} - 1} - 1\right)}{\left(x^{2} - 1\right)^{5} \left(\frac{x^{2}}{\left(x^{2} - 1\right)^{4}} + 1\right)^{2}} + \frac{6 x \left(\frac{4 x^{2}}{x^{2} - 1} - 1\right)^{3}}{\left(x^{2} - 1\right)^{8} \left(\frac{x^{2}}{\left(x^{2} - 1\right)^{4}} + 1\right)^{3}} - 3 - \frac{12 \left(\frac{16 x^{4}}{\left(x^{2} - 1\right)^{2}} - \frac{12 x^{2}}{x^{2} - 1} + 1\right) \operatorname{atan}{\left(\frac{x}{\left(x^{2} - 1\right)^{2}} \right)}}{\left(x^{2} - 1\right)^{3} \left(\frac{x^{2}}{\left(x^{2} - 1\right)^{4}} + 1\right)} + \frac{2 \left(\frac{4 x^{2}}{x^{2} - 1} - 1\right) \left(\frac{40 x^{4}}{\left(x^{2} - 1\right)^{2}} - \frac{20 x^{2}}{x^{2} - 1} + 1\right) \operatorname{atan}{\left(\frac{x}{\left(x^{2} - 1\right)^{2}} \right)}}{\left(x^{2} - 1\right)^{6} \left(\frac{x^{2}}{\left(x^{2} - 1\right)^{4}} + 1\right)^{2}}\right)
Simplificar
Gráfico
Derivada de x*sqr(1-x^2)+arctg(x/sqr(1-x^2))
    © Sr Examen – Калькулятор