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

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

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    /          ___        \
    |        \/ x         |
atan|---------------------|
    |        _____________|
    |       /    ________ |
    |    3 /    /      2  |
    \2 + \/   \/  1 - x   /
atan⁡(x1−x23+2)\operatorname{atan}{\left(\frac{\sqrt{x}}{\sqrt[3]{\sqrt{1 - x^{2}}} + 2} \right)} 
atan(sqrt(x)/(2 + (sqrt(1 - x^2))^(1/3)))
Gráfica
02468-8-6-4-2-10100.01.0
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                                                    3/2                 
               1                                   x                    
------------------------------- + --------------------------------------
        /        _____________\                                        2
        |       /    ________ |                 /        _____________\ 
    ___ |    3 /    /      2  |             5/6 |       /    ________ | 
2*\/ x *\2 + \/   \/  1 - x   /     /     2\    |    3 /    /      2  | 
                                  3*\1 - x /   *\2 + \/   \/  1 - x   / 
------------------------------------------------------------------------
                                     x                                  
                      1 + ------------------------                      
                                                 2                      
                          /        _____________\                       
                          |       /    ________ |                       
                          |    3 /    /      2  |                       
                          \2 + \/   \/  1 - x   /
x323(1−x2)56(1−x23+2)2+12x(1−x23+2)x(1−x23+2)2+1\frac{\frac{x^{\frac{3}{2}}}{3 \left(1 - x^{2}\right)^{\frac{5}{6}} \left(\sqrt[3]{\sqrt{1 - x^{2}}} + 2\right)^{2}} + \frac{1}{2 \sqrt{x} \left(\sqrt[3]{\sqrt{1 - x^{2}}} + 2\right)}}{\frac{x}{\left(\sqrt[3]{\sqrt{1 - x^{2}}} + 2\right)^{2}} + 1}
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Segunda derivada [src] 
                                                                                                             /                    2            \ /                       3/2           \
                                                                                                             |                 2*x             | |  3                 2*x              |
                                                                                                           2*|3 + -----------------------------|*|----- + -----------------------------|
                                                                                                             |            5/6 /       ________\| |  ___           5/6 /       ________\|
                        5/2                              5/2                               ___               |    /     2\    |    6 /      2 || |\/ x    /     2\    |    6 /      2 ||
   9                 8*x                             20*x                             24*\/ x                \    \1 - x /   *\2 + \/  1 - x  // \        \1 - x /   *\2 + \/  1 - x  //
- ---- + ------------------------------ + ------------------------------ + ----------------------------- - -----------------------------------------------------------------------------
   3/2                                2           11/6 /       ________\           5/6 /       ________\                                                              2                 
  x              5/3 /       ________\    /     2\     |    6 /      2 |   /     2\    |    6 /      2 |                                             /       ________\                  
         /     2\    |    6 /      2 |    \1 - x /    *\2 + \/  1 - x  /   \1 - x /   *\2 + \/  1 - x  /                    /            x         \ |    6 /      2 |                  
         \1 - x /   *\2 + \/  1 - x  /                                                                                      |1 + ------------------|*\2 + \/  1 - x  /                  
                                                                                                                            |                     2|                                    
                                                                                                                            |    /       ________\ |                                    
                                                                                                                            |    |    6 /      2 | |                                    
                                                                                                                            \    \2 + \/  1 - x  / /                                    
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                 /       ________\                                                                      
                                                                        /            x         \ |    6 /      2 |                                                                      
                                                                     36*|1 + ------------------|*\2 + \/  1 - x  /                                                                      
                                                                        |                     2|                                                                                        
                                                                        |    /       ________\ |                                                                                        
                                                                        |    |    6 /      2 | |                                                                                        
                                                                        \    \2 + \/  1 - x  / /
8x52(1−x2)53(1−x26+2)2+20x52(1−x2)116(1−x26+2)+24x(1−x2)56(1−x26+2)−2(2x32(1−x2)56(1−x26+2)+3x)(2x2(1−x2)56(1−x26+2)+3)(x(1−x26+2)2+1)(1−x26+2)2−9x3236(x(1−x26+2)2+1)(1−x26+2)\frac{\frac{8 x^{\frac{5}{2}}}{\left(1 - x^{2}\right)^{\frac{5}{3}} \left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} + \frac{20 x^{\frac{5}{2}}}{\left(1 - x^{2}\right)^{\frac{11}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} + \frac{24 \sqrt{x}}{\left(1 - x^{2}\right)^{\frac{5}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} - \frac{2 \left(\frac{2 x^{\frac{3}{2}}}{\left(1 - x^{2}\right)^{\frac{5}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} + \frac{3}{\sqrt{x}}\right) \left(\frac{2 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} + 3\right)}{\left(\frac{x}{\left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} + 1\right) \left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} - \frac{9}{x^{\frac{3}{2}}}}{36 \left(\frac{x}{\left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} + 1\right) \left(\sqrt[6]{1 - x^{2}} + 2\right)}
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Tercera derivada [src] 
                                                                                                                                                                                                                               /                    2            \ /                        5/2                              5/2                               ___          \                                      2                                                                                                                                                 
                                                                                                                                                                                                                               |                 2*x             | |   9                 8*x                             20*x                             24*\/ x           |   /                    2            \  /                       3/2           \     /                       3/2           \ /                     2                       2            \
                                                                                                                                                                                                                               |3 + -----------------------------|*|- ---- + ------------------------------ + ------------------------------ + -----------------------------|   |                 2*x             |  |  3                 2*x              |     |  3                 2*x              | |     9            5*x                     3*x             |
                                                                                                                                                                                                                               |            5/6 /       ________\| |   3/2                                2           11/6 /       ________\           5/6 /       ________\|   |3 + -----------------------------| *|----- + -----------------------------|   x*|----- + -----------------------------|*|----------- + ------------ + -----------------------------|
                                                                                                                                                                                                                               |    /     2\    |    6 /      2 || |  x              5/3 /       ________\    /     2\     |    6 /      2 |   /     2\    |    6 /      2 ||   |            5/6 /       ________\|  |  ___           5/6 /       ________\|     |  ___           5/6 /       ________\| |        5/6           11/6           5/3 /       ________\|
                       3/2                                                                        7/2                                3/2                                7/2                                 7/2                \    \1 - x /   *\2 + \/  1 - x  // |         /     2\    |    6 /      2 |    \1 - x /    *\2 + \/  1 - x  /   \1 - x /   *\2 + \/  1 - x  /|   |    /     2\    |    6 /      2 ||  |\/ x    /     2\    |    6 /      2 ||     |\/ x    /     2\    |    6 /      2 || |/     2\      /     2\       /     2\    |    6 /      2 ||
  3                   x                                     1                                  2*x                                5*x                               10*x                                55*x                                                       \         \1 - x /   *\2 + \/  1 - x  /                                                                  /   \    \1 - x /   *\2 + \/  1 - x  //  \        \1 - x /   *\2 + \/  1 - x  //     \        \1 - x /   *\2 + \/  1 - x  // \\1 - x /      \1 - x /       \1 - x /   *\2 + \/  1 - x  //
------ + ------------------------------ + ------------------------------------- + -------------------------------- + -------------------------------- + -------------------------------- + --------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------
   5/2                                2                   5/6 /       ________\                                  3             11/6 /       ________\                                  2              17/6 /       ________\                                                                                                2                                                                                                               4                                                                                           3                            
8*x              5/3 /       ________\        ___ /     2\    |    6 /      2 |             5/2 /       ________\      /     2\     |    6 /      2 |             8/3 /       ________\       /     2\     |    6 /      2 |                                                                               /       ________\                                                                                             2 /       ________\                                                                           /       ________\                             
         /     2\    |    6 /      2 |    4*\/ x *\1 - x /   *\2 + \/  1 - x  /     /     2\    |    6 /      2 |    2*\1 - x /    *\2 + \/  1 - x  /     /     2\    |    6 /      2 |    27*\1 - x /    *\2 + \/  1 - x  /                                                      /            x         \ |    6 /      2 |                                                                     /            x         \  |    6 /      2 |                                                  /            x         \ |    6 /      2 |                             
         \1 - x /   *\2 + \/  1 - x  /                                            9*\1 - x /   *\2 + \/  1 - x  /                                       9*\1 - x /   *\2 + \/  1 - x  /                                                                                        54*|1 + ------------------|*\2 + \/  1 - x  /                                                                  27*|1 + ------------------| *\2 + \/  1 - x  /                                               27*|1 + ------------------|*\2 + \/  1 - x  /                             
                                                                                                                                                                                                                                                                                  |                     2|                                                                                       |                     2|                                                                     |                     2|                                               
                                                                                                                                                                                                                                                                                  |    /       ________\ |                                                                                       |    /       ________\ |                                                                     |    /       ________\ |                                               
                                                                                                                                                                                                                                                                                  |    |    6 /      2 | |                                                                                       |    |    6 /      2 | |                                                                     |    |    6 /      2 | |                                               
                                                                                                                                                                                                                                                                                  \    \2 + \/  1 - x  / /                                                                                       \    \2 + \/  1 - x  / /                                                                     \    \2 + \/  1 - x  / /                                               
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                       /       ________\                                                                                                                                                                                                                                                             
                                                                                                                                                                                                                                                              /            x         \ |    6 /      2 |                                                                                                                                                                                                                                                             
                                                                                                                                                                                                                                                              |1 + ------------------|*\2 + \/  1 - x  /                                                                                                                                                                                                                                                             
                                                                                                                                                                                                                                                              |                     2|                                                                                                                                                                                                                                                                               
                                                                                                                                                                                                                                                              |    /       ________\ |                                                                                                                                                                                                                                                                               
                                                                                                                                                                                                                                                              |    |    6 /      2 | |                                                                                                                                                                                                                                                                               
                                                                                                                                                                                                                                                              \    \2 + \/  1 - x  / /
2x729(1−x2)52(1−x26+2)3+10x729(1−x2)83(1−x26+2)2+55x7227(1−x2)176(1−x26+2)+x32(1−x2)53(1−x26+2)2+5x322(1−x2)116(1−x26+2)−x(2x32(1−x2)56(1−x26+2)+3x)(3x2(1−x2)53(1−x26+2)+5x2(1−x2)116+9(1−x2)56)27(x(1−x26+2)2+1)(1−x26+2)3−(2x2(1−x2)56(1−x26+2)+3)(8x52(1−x2)53(1−x26+2)2+20x52(1−x2)116(1−x26+2)+24x(1−x2)56(1−x26+2)−9x32)54(x(1−x26+2)2+1)(1−x26+2)2+(2x32(1−x2)56(1−x26+2)+3x)(2x2(1−x2)56(1−x26+2)+3)227(x(1−x26+2)2+1)2(1−x26+2)4+14x(1−x2)56(1−x26+2)+38x52(x(1−x26+2)2+1)(1−x26+2)\frac{\frac{2 x^{\frac{7}{2}}}{9 \left(1 - x^{2}\right)^{\frac{5}{2}} \left(\sqrt[6]{1 - x^{2}} + 2\right)^{3}} + \frac{10 x^{\frac{7}{2}}}{9 \left(1 - x^{2}\right)^{\frac{8}{3}} \left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} + \frac{55 x^{\frac{7}{2}}}{27 \left(1 - x^{2}\right)^{\frac{17}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} + \frac{x^{\frac{3}{2}}}{\left(1 - x^{2}\right)^{\frac{5}{3}} \left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} + \frac{5 x^{\frac{3}{2}}}{2 \left(1 - x^{2}\right)^{\frac{11}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} - \frac{x \left(\frac{2 x^{\frac{3}{2}}}{\left(1 - x^{2}\right)^{\frac{5}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} + \frac{3}{\sqrt{x}}\right) \left(\frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{3}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} + \frac{5 x^{2}}{\left(1 - x^{2}\right)^{\frac{11}{6}}} + \frac{9}{\left(1 - x^{2}\right)^{\frac{5}{6}}}\right)}{27 \left(\frac{x}{\left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} + 1\right) \left(\sqrt[6]{1 - x^{2}} + 2\right)^{3}} - \frac{\left(\frac{2 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} + 3\right) \left(\frac{8 x^{\frac{5}{2}}}{\left(1 - x^{2}\right)^{\frac{5}{3}} \left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} + \frac{20 x^{\frac{5}{2}}}{\left(1 - x^{2}\right)^{\frac{11}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} + \frac{24 \sqrt{x}}{\left(1 - x^{2}\right)^{\frac{5}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} - \frac{9}{x^{\frac{3}{2}}}\right)}{54 \left(\frac{x}{\left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} + 1\right) \left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} + \frac{\left(\frac{2 x^{\frac{3}{2}}}{\left(1 - x^{2}\right)^{\frac{5}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} + \frac{3}{\sqrt{x}}\right) \left(\frac{2 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} + 3\right)^{2}}{27 \left(\frac{x}{\left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} + 1\right)^{2} \left(\sqrt[6]{1 - x^{2}} + 2\right)^{4}} + \frac{1}{4 \sqrt{x} \left(1 - x^{2}\right)^{\frac{5}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} + \frac{3}{8 x^{\frac{5}{2}}}}{\left(\frac{x}{\left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} + 1\right) \left(\sqrt[6]{1 - x^{2}} + 2\right)}
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Gráfico
Derivada de y=arctg((√x)/(2+(√(1-x^2)^(1/3))))
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