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y=ctg^3x*arctg^3x
Derivada de la función/ tg^3x/ y=ctg/ arctg/ y=ctg^3x*arctg^3x

Derivada de y=ctg^3x*arctg^3x

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   3        3   
cot (x)*atan (x)
cot⁡3(x)atan⁡3(x)\cot^{3}{\left(x \right)} \operatorname{atan}^{3}{\left(x \right)} 
cot(x)^3*atan(x)^3
Gráfica
02468-8-6-4-2-1010-10000000001000000000
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Trazar el gráfico f'(x)
Primera derivada [src] 
                                          2       3   
    3       2    /          2   \   3*atan (x)*cot (x)
atan (x)*cot (x)*\-3 - 3*cot (x)/ + ------------------
                                               2      
                                          1 + x
(−3cot⁡2(x)−3)cot⁡2(x)atan⁡3(x)+3cot⁡3(x)atan⁡2(x)x2+1\left(- 3 \cot^{2}{\left(x \right)} - 3\right) \cot^{2}{\left(x \right)} \operatorname{atan}^{3}{\left(x \right)} + \frac{3 \cot^{3}{\left(x \right)} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1}
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Segunda derivada [src] 
  /                                            2                         /       2   \               \               
  |    2    /       2   \ /         2   \   cot (x)*(-1 + x*atan(x))   3*\1 + cot (x)/*atan(x)*cot(x)|               
6*|atan (x)*\1 + cot (x)/*\1 + 2*cot (x)/ - ------------------------ - ------------------------------|*atan(x)*cot(x)
  |                                                        2                            2            |               
  |                                                /     2\                        1 + x             |               
  \                                                \1 + x /                                          /
6((cot⁡2(x)+1)(2cot⁡2(x)+1)atan⁡2(x)−3(cot⁡2(x)+1)cot⁡(x)atan⁡(x)x2+1−(xatan⁡(x)−1)cot⁡2(x)(x2+1)2)cot⁡(x)atan⁡(x)6 \left(\left(\cot^{2}{\left(x \right)} + 1\right) \left(2 \cot^{2}{\left(x \right)} + 1\right) \operatorname{atan}^{2}{\left(x \right)} - \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \frac{\left(x \operatorname{atan}{\left(x \right)} - 1\right) \cot^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\right) \cot{\left(x \right)} \operatorname{atan}{\left(x \right)}
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Tercera derivada [src] 
  /        /                                     2     2   \                                                                                                                                                                                     \
  |   3    |  1          2      6*x*atan(x)   4*x *atan (x)|                                                                                                                                                                                     |
  |cot (x)*|------ - atan (x) - ----------- + -------------|                                                                                                                                                                                     |
  |        |     2                      2              2   |                          /             2                                      \         2    /       2   \ /         2   \               2    /       2   \                         |
  |        \1 + x                  1 + x          1 + x    /       3    /       2   \ |/       2   \         4           2    /       2   \|   9*atan (x)*\1 + cot (x)/*\1 + 2*cot (x)/*cot(x)   9*cot (x)*\1 + cot (x)/*(-1 + x*atan(x))*atan(x)|
6*|--------------------------------------------------------- - atan (x)*\1 + cot (x)/*\\1 + cot (x)/  + 2*cot (x) + 7*cot (x)*\1 + cot (x)// + ----------------------------------------------- + ------------------------------------------------|
  |                                2                                                                                                                                     2                                                  2                    |
  |                        /     2\                                                                                                                                 1 + x                                           /     2\                     |
  \                        \1 + x /                                                                                                                                                                                 \1 + x /                     /
6(−(cot⁡2(x)+1)((cot⁡2(x)+1)2+7(cot⁡2(x)+1)cot⁡2(x)+2cot⁡4(x))atan⁡3(x)+9(cot⁡2(x)+1)(2cot⁡2(x)+1)cot⁡(x)atan⁡2(x)x2+1+9(xatan⁡(x)−1)(cot⁡2(x)+1)cot⁡2(x)atan⁡(x)(x2+1)2+(4x2atan⁡2(x)x2+1−6xatan⁡(x)x2+1−atan⁡2(x)+1x2+1)cot⁡3(x)(x2+1)2)6 \left(- \left(\cot^{2}{\left(x \right)} + 1\right) \left(\left(\cot^{2}{\left(x \right)} + 1\right)^{2} + 7 \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{2}{\left(x \right)} + 2 \cot^{4}{\left(x \right)}\right) \operatorname{atan}^{3}{\left(x \right)} + \frac{9 \left(\cot^{2}{\left(x \right)} + 1\right) \left(2 \cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{9 \left(x \operatorname{atan}{\left(x \right)} - 1\right) \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{2}{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{\left(\frac{4 x^{2} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{6 x \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \operatorname{atan}^{2}{\left(x \right)} + \frac{1}{x^{2} + 1}\right) \cot^{3}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\right)
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Gráfico
Derivada de y=ctg^3x*arctg^3x
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