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y=arctg((3x-x^3)/(1-3x^2))
Derivada de la función/ x-x^3/ arctg/ -3x^2/ y=arctg((3x-x^3)/(1-3x^2))

Derivada de y=arctg((3x-x^3)/(1-3x^2))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
    /       3\
    |3*x - x |
atan|--------|
    |       2|
    \1 - 3*x /
atan⁡(−x3+3x1−3x2)\operatorname{atan}{\left(\frac{- x^{3} + 3 x}{1 - 3 x^{2}} \right)} 
atan((3*x - x^3)/(1 - 3*x^2))
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
       2       /       3\
3 - 3*x    6*x*\3*x - x /
-------- + --------------
       2              2  
1 - 3*x     /       2\   
            \1 - 3*x /   
-------------------------
                   2     
         /       3\      
         \3*x - x /      
     1 + -----------     
                   2     
         /       2\      
         \1 - 3*x /
6x(−x3+3x)(1−3x2)2+3−3x21−3x21+(−x3+3x)2(1−3x2)2\frac{\frac{6 x \left(- x^{3} + 3 x\right)}{\left(1 - 3 x^{2}\right)^{2}} + \frac{3 - 3 x^{2}}{1 - 3 x^{2}}}{1 + \frac{\left(- x^{3} + 3 x\right)^{2}}{\left(1 - 3 x^{2}\right)^{2}}}
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Segunda derivada [src] 
    /                                                                           2          \
    |                                                  /            2 /      2\\           |
    |                                                  |     2   2*x *\-3 + x /|  /      2\|
    |                                                3*|1 - x  + --------------| *\-3 + x /|
    |           2      /      2\       2 /      2\     |                   2   |           |
    |     -3 + x     6*\-1 + x /   12*x *\-3 + x /     \           -1 + 3*x    /           |
6*x*|1 - --------- - ----------- + --------------- - --------------------------------------|
    |            2            2                 2       /                2\                |
    |    -1 + 3*x     -1 + 3*x       /        2\        |     2 /      2\ |            2   |
    |                                \-1 + 3*x /        |    x *\-3 + x / | /        2\    |
    |                                                   |1 + -------------|*\-1 + 3*x /    |
    |                                                   |                2|                |
    |                                                   |     /        2\ |                |
    \                                                   \     \-1 + 3*x / /                /
--------------------------------------------------------------------------------------------
                              /                2\                                           
                              |     2 /      2\ |                                           
                              |    x *\-3 + x / | /        2\                               
                              |1 + -------------|*\-1 + 3*x /                               
                              |                2|                                           
                              |     /        2\ |                                           
                              \     \-1 + 3*x / /
6x(12x2(x2−3)(3x2−1)2−x2−33x2−1−3(x2−3)(2x2(x2−3)3x2−1−x2+1)2(3x2−1)2(x2(x2−3)2(3x2−1)2+1)−6(x2−1)3x2−1+1)(3x2−1)(x2(x2−3)2(3x2−1)2+1)\frac{6 x \left(\frac{12 x^{2} \left(x^{2} - 3\right)}{\left(3 x^{2} - 1\right)^{2}} - \frac{x^{2} - 3}{3 x^{2} - 1} - \frac{3 \left(x^{2} - 3\right) \left(\frac{2 x^{2} \left(x^{2} - 3\right)}{3 x^{2} - 1} - x^{2} + 1\right)^{2}}{\left(3 x^{2} - 1\right)^{2} \left(\frac{x^{2} \left(x^{2} - 3\right)^{2}}{\left(3 x^{2} - 1\right)^{2}} + 1\right)} - \frac{6 \left(x^{2} - 1\right)}{3 x^{2} - 1} + 1\right)}{\left(3 x^{2} - 1\right) \left(\frac{x^{2} \left(x^{2} - 3\right)^{2}}{\left(3 x^{2} - 1\right)^{2}} + 1\right)}
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Tercera derivada [src] 
  /                                                                                                                  /                                              2                  2                            \                                                                                                                                          \
  |                                                                                        /            2 /      2\\ |           2                       2 /      2\        4 /      2\        2 /      2\ /      2\|                                             3                   /            2 /      2\\ /           2      /      2\       2 /      2\\|
  |                                                                                        |     2   2*x *\-3 + x /| |  /      2\       2 /      2\   2*x *\-3 + x /    36*x *\-3 + x /    24*x *\-1 + x /*\-3 + x /|                  2 /            2 /      2\\        2 /      2\ |     2   2*x *\-3 + x /| |     -3 + x     6*\-1 + x /   12*x *\-3 + x /||
  |                                                                                      3*|1 - x  + --------------|*|3*\-1 + x /  + 2*x *\-3 + x / - --------------- + ---------------- - -------------------------|       2 /      2\  |     2   2*x *\-3 + x /|    12*x *\-3 + x /*|1 - x  + --------------|*|1 - --------- - ----------- + ---------------||
  |                                                                                        |                   2   | |                                           2                   2                     2        |   36*x *\-3 + x / *|1 - x  + --------------|                    |                   2   | |            2            2                 2 ||
  |          2       /      2\        4 /      2\       2 /      2\        2 /      2\     \           -1 + 3*x    / |                                   -1 + 3*x         /        2\              -1 + 3*x         |                    |                   2   |                    \           -1 + 3*x    / |    -1 + 3*x     -1 + 3*x       /        2\  ||
  |      18*x      9*\-1 + x /   216*x *\-3 + x /   36*x *\-3 + x /   108*x *\-1 + x /                               \                                                    \-1 + 3*x /                               /                    \           -1 + 3*x    /                                              \                                \-1 + 3*x /  /|
6*|1 - --------- - ----------- - ---------------- + --------------- + ---------------- + ---------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------- + -----------------------------------------------------------------------------------------|
  |            2            2                 3                  2                 2                                                   /                2\                                                                                      2                                                  /                2\                                         |
  |    -1 + 3*x     -1 + 3*x       /        2\        /        2\       /        2\                                                    |     2 /      2\ |            2                                                      /                2\                                                   |     2 /      2\ |            2                            |
  |                                \-1 + 3*x /        \-1 + 3*x /       \-1 + 3*x /                                                    |    x *\-3 + x / | /        2\                                                       |     2 /      2\ |             4                                     |    x *\-3 + x / | /        2\                             |
  |                                                                                                                                    |1 + -------------|*\-1 + 3*x /                                                       |    x *\-3 + x / |  /        2\                                      |1 + -------------|*\-1 + 3*x /                             |
  |                                                                                                                                    |                2|                                                                   |1 + -------------| *\-1 + 3*x /                                      |                2|                                         |
  |                                                                                                                                    |     /        2\ |                                                                   |                2|                                                   |     /        2\ |                                         |
  |                                                                                                                                    \     \-1 + 3*x / /                                                                   |     /        2\ |                                                   \     \-1 + 3*x / /                                         |
  \                                                                                                                                                                                                                          \     \-1 + 3*x / /                                                                                                               /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                /                2\                                                                                                                                                                             
                                                                                                                                                                |     2 /      2\ |                                                                                                                                                                             
                                                                                                                                                                |    x *\-3 + x / | /        2\                                                                                                                                                                 
                                                                                                                                                                |1 + -------------|*\-1 + 3*x /                                                                                                                                                                 
                                                                                                                                                                |                2|                                                                                                                                                                             
                                                                                                                                                                |     /        2\ |                                                                                                                                                                             
                                                                                                                                                                \     \-1 + 3*x / /
6(−216x4(x2−3)(3x2−1)3−36x2(x2−3)2(2x2(x2−3)3x2−1−x2+1)3(3x2−1)4(x2(x2−3)2(3x2−1)2+1)2+36x2(x2−3)(3x2−1)2+12x2(x2−3)(2x2(x2−3)3x2−1−x2+1)(12x2(x2−3)(3x2−1)2−x2−33x2−1−6(x2−1)3x2−1+1)(3x2−1)2(x2(x2−3)2(3x2−1)2+1)+108x2(x2−1)(3x2−1)2−18x23x2−1−9(x2−1)3x2−1+1+3(2x2(x2−3)3x2−1−x2+1)(36x4(x2−3)2(3x2−1)2−2x2(x2−3)23x2−1−24x2(x2−3)(x2−1)3x2−1+2x2(x2−3)+3(x2−1)2)(3x2−1)2(x2(x2−3)2(3x2−1)2+1))(3x2−1)(x2(x2−3)2(3x2−1)2+1)\frac{6 \left(- \frac{216 x^{4} \left(x^{2} - 3\right)}{\left(3 x^{2} - 1\right)^{3}} - \frac{36 x^{2} \left(x^{2} - 3\right)^{2} \left(\frac{2 x^{2} \left(x^{2} - 3\right)}{3 x^{2} - 1} - x^{2} + 1\right)^{3}}{\left(3 x^{2} - 1\right)^{4} \left(\frac{x^{2} \left(x^{2} - 3\right)^{2}}{\left(3 x^{2} - 1\right)^{2}} + 1\right)^{2}} + \frac{36 x^{2} \left(x^{2} - 3\right)}{\left(3 x^{2} - 1\right)^{2}} + \frac{12 x^{2} \left(x^{2} - 3\right) \left(\frac{2 x^{2} \left(x^{2} - 3\right)}{3 x^{2} - 1} - x^{2} + 1\right) \left(\frac{12 x^{2} \left(x^{2} - 3\right)}{\left(3 x^{2} - 1\right)^{2}} - \frac{x^{2} - 3}{3 x^{2} - 1} - \frac{6 \left(x^{2} - 1\right)}{3 x^{2} - 1} + 1\right)}{\left(3 x^{2} - 1\right)^{2} \left(\frac{x^{2} \left(x^{2} - 3\right)^{2}}{\left(3 x^{2} - 1\right)^{2}} + 1\right)} + \frac{108 x^{2} \left(x^{2} - 1\right)}{\left(3 x^{2} - 1\right)^{2}} - \frac{18 x^{2}}{3 x^{2} - 1} - \frac{9 \left(x^{2} - 1\right)}{3 x^{2} - 1} + 1 + \frac{3 \left(\frac{2 x^{2} \left(x^{2} - 3\right)}{3 x^{2} - 1} - x^{2} + 1\right) \left(\frac{36 x^{4} \left(x^{2} - 3\right)^{2}}{\left(3 x^{2} - 1\right)^{2}} - \frac{2 x^{2} \left(x^{2} - 3\right)^{2}}{3 x^{2} - 1} - \frac{24 x^{2} \left(x^{2} - 3\right) \left(x^{2} - 1\right)}{3 x^{2} - 1} + 2 x^{2} \left(x^{2} - 3\right) + 3 \left(x^{2} - 1\right)^{2}\right)}{\left(3 x^{2} - 1\right)^{2} \left(\frac{x^{2} \left(x^{2} - 3\right)^{2}}{\left(3 x^{2} - 1\right)^{2}} + 1\right)}\right)}{\left(3 x^{2} - 1\right) \left(\frac{x^{2} \left(x^{2} - 3\right)^{2}}{\left(3 x^{2} - 1\right)^{2}} + 1\right)}
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Gráfico
Derivada de y=arctg((3x-x^3)/(1-3x^2))
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