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

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

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

Gráfico:

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Solución

Ha introducido [src] 
    /        3    \
    |   2   x     |
acot|2*x  + -- - 1|
    \       2     /
acot⁡((x32+2x2)−1)\operatorname{acot}{\left(\left(\frac{x^{3}}{2} + 2 x^{2}\right) - 1 \right)} 
acot(2*x^2 + x^3/2 - 1)
Gráfica
02468-8-6-4-2-1010-1010
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    /         2\    
    |      3*x |    
   -|4*x + ----|    
    \       2  /    
--------------------
                   2
    /        3    \ 
    |   2   x     | 
1 + |2*x  + -- - 1| 
    \       2     /
−3x22+4x((x32+2x2)−1)2+1- \frac{\frac{3 x^{2}}{2} + 4 x}{\left(\left(\frac{x^{3}}{2} + 2 x^{2}\right) - 1\right)^{2} + 1}
Simplificar
Segunda derivada [src] 
  /            2          2 /      3      2\\
  |           x *(8 + 3*x) *\-2 + x  + 4*x /|
4*|-4 - 3*x + ------------------------------|
  |                                   2     |
  |                   /      3      2\      |
  \               4 + \-2 + x  + 4*x /      /
---------------------------------------------
                                2            
                /      3      2\             
            4 + \-2 + x  + 4*x /
4(x2(3x+8)2(x3+4x2−2)(x3+4x2−2)2+4−3x−4)(x3+4x2−2)2+4\frac{4 \left(\frac{x^{2} \left(3 x + 8\right)^{2} \left(x^{3} + 4 x^{2} - 2\right)}{\left(x^{3} + 4 x^{2} - 2\right)^{2} + 4} - 3 x - 4\right)}{\left(x^{3} + 4 x^{2} - 2\right)^{2} + 4}
Simplificar
Tercera derivada [src] 
  /                                                             2                                           \
  |          3          3          3          3 /      3      2\                            /      3      2\|
  |         x *(8 + 3*x)        4*x *(8 + 3*x) *\-2 + x  + 4*x /    6*x*(4 + 3*x)*(8 + 3*x)*\-2 + x  + 4*x /|
4*|-3 + --------------------- - --------------------------------- + ----------------------------------------|
  |                         2                               2                                    2          |
  |         /      3      2\         /                    2\                     /      3      2\           |
  |     4 + \-2 + x  + 4*x /         |    /      3      2\ |                 4 + \-2 + x  + 4*x /           |
  \                                  \4 + \-2 + x  + 4*x / /                                                /
-------------------------------------------------------------------------------------------------------------
                                                                2                                            
                                                /      3      2\                                             
                                            4 + \-2 + x  + 4*x /
4(x3(3x+8)3(x3+4x2−2)2+4−4x3(3x+8)3(x3+4x2−2)2((x3+4x2−2)2+4)2+6x(3x+4)(3x+8)(x3+4x2−2)(x3+4x2−2)2+4−3)(x3+4x2−2)2+4\frac{4 \left(\frac{x^{3} \left(3 x + 8\right)^{3}}{\left(x^{3} + 4 x^{2} - 2\right)^{2} + 4} - \frac{4 x^{3} \left(3 x + 8\right)^{3} \left(x^{3} + 4 x^{2} - 2\right)^{2}}{\left(\left(x^{3} + 4 x^{2} - 2\right)^{2} + 4\right)^{2}} + \frac{6 x \left(3 x + 4\right) \left(3 x + 8\right) \left(x^{3} + 4 x^{2} - 2\right)}{\left(x^{3} + 4 x^{2} - 2\right)^{2} + 4} - 3\right)}{\left(x^{3} + 4 x^{2} - 2\right)^{2} + 4}
Simplificar
Gráfico
Derivada de y=arcctg(2x^2+1/2x^3-1)
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