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

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

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    /   ________\
    |3 /  2     |
atan\\/  x  - 2 /
atan⁡(x2−23)\operatorname{atan}{\left(\sqrt[3]{x^{2} - 2} \right)} 
atan((x^2 - 2)^(1/3))
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
              2*x              
-------------------------------
  /            2/3\         2/3
  |    / 2    \   | / 2    \   
3*\1 + \x  - 2/   /*\x  - 2/
2x3(x2−2)23((x2−2)23+1)\frac{2 x}{3 \left(x^{2} - 2\right)^{\frac{2}{3}} \left(\left(x^{2} - 2\right)^{\frac{2}{3}} + 1\right)}
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Segunda derivada [src] 
  /                      2                      2            \
  |     3             4*x                    4*x             |
2*|------------ - ------------ - ----------------------------|
  |         2/3            5/3   /             2/3\          |
  |/      2\      /      2\      |    /      2\   | /      2\|
  \\-2 + x /      \-2 + x /      \1 + \-2 + x /   /*\-2 + x //
--------------------------------------------------------------
                       /             2/3\                     
                       |    /      2\   |                     
                     9*\1 + \-2 + x /   /
2(−4x2(x2−2)((x2−2)23+1)−4x2(x2−2)53+3(x2−2)23)9((x2−2)23+1)\frac{2 \left(- \frac{4 x^{2}}{\left(x^{2} - 2\right) \left(\left(x^{2} - 2\right)^{\frac{2}{3}} + 1\right)} - \frac{4 x^{2}}{\left(x^{2} - 2\right)^{\frac{5}{3}}} + \frac{3}{\left(x^{2} - 2\right)^{\frac{2}{3}}}\right)}{9 \left(\left(x^{2} - 2\right)^{\frac{2}{3}} + 1\right)}
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Tercera derivada [src] 
    /                                                       2                        2                                 2            \
    |       9                      9                    10*x                      8*x                              10*x             |
8*x*|- ------------ - ---------------------------- + ------------ + -------------------------------- + -----------------------------|
    |           5/3   /             2/3\                      8/3                     2                /             2/3\          2|
    |  /      2\      |    /      2\   | /      2\   /      2\      /             2/3\           4/3   |    /      2\   | /      2\ |
    |  \-2 + x /      \1 + \-2 + x /   /*\-2 + x /   \-2 + x /      |    /      2\   |  /      2\      \1 + \-2 + x /   /*\-2 + x / |
    \                                                               \1 + \-2 + x /   / *\-2 + x /                                   /
-------------------------------------------------------------------------------------------------------------------------------------
                                                           /             2/3\                                                        
                                                           |    /      2\   |                                                        
                                                        27*\1 + \-2 + x /   /
8x(10x2(x2−2)2((x2−2)23+1)+8x2(x2−2)43((x2−2)23+1)2+10x2(x2−2)83−9(x2−2)((x2−2)23+1)−9(x2−2)53)27((x2−2)23+1)\frac{8 x \left(\frac{10 x^{2}}{\left(x^{2} - 2\right)^{2} \left(\left(x^{2} - 2\right)^{\frac{2}{3}} + 1\right)} + \frac{8 x^{2}}{\left(x^{2} - 2\right)^{\frac{4}{3}} \left(\left(x^{2} - 2\right)^{\frac{2}{3}} + 1\right)^{2}} + \frac{10 x^{2}}{\left(x^{2} - 2\right)^{\frac{8}{3}}} - \frac{9}{\left(x^{2} - 2\right) \left(\left(x^{2} - 2\right)^{\frac{2}{3}} + 1\right)} - \frac{9}{\left(x^{2} - 2\right)^{\frac{5}{3}}}\right)}{27 \left(\left(x^{2} - 2\right)^{\frac{2}{3}} + 1\right)}
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Gráfico
Derivada de arctg((x^2-2)^1/3)
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