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y=ctg^3*(4x)*arctg*(2x)^3
Derivada de la función/ arctg/ y=ctg/ (2x)^3/ y=ctg^3*(4x)*arctg*(2x)^3

Derivada de y=ctg^3*(4x)*arctg*(2x)^3

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

Gráfico:

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Solución

Ha introducido [src] 
   3          3     
cot (4*x)*atan (2*x)
cot⁡3(4x)atan⁡3(2x)\cot^{3}{\left(4 x \right)} \operatorname{atan}^{3}{\left(2 x \right)} 
cot(4*x)^3*atan(2*x)^3
Gráfica
02468-8-6-4-2-1010-2500000025000000
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Primera derivada [src] 
                                                  2         3     
    3         2      /            2     \   6*atan (2*x)*cot (4*x)
atan (2*x)*cot (4*x)*\-12 - 12*cot (4*x)/ + ----------------------
                                                          2       
                                                   1 + 4*x
(−12cot⁡2(4x)−12)cot⁡2(4x)atan⁡3(2x)+6cot⁡3(4x)atan⁡2(2x)4x2+1\left(- 12 \cot^{2}{\left(4 x \right)} - 12\right) \cot^{2}{\left(4 x \right)} \operatorname{atan}^{3}{\left(2 x \right)} + \frac{6 \cot^{3}{\left(4 x \right)} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1}
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Segunda derivada [src] 
   /     2                                                                                /       2     \                   \                   
   |  cot (4*x)*(-1 + 2*x*atan(2*x))         2      /       2     \ /         2     \   6*\1 + cot (4*x)/*atan(2*x)*cot(4*x)|                   
24*|- ------------------------------ + 4*atan (2*x)*\1 + cot (4*x)/*\1 + 2*cot (4*x)/ - ------------------------------------|*atan(2*x)*cot(4*x)
   |                     2                                                                                   2              |                   
   |           /       2\                                                                             1 + 4*x               |                   
   \           \1 + 4*x /                                                                                                   /
24(4(cot⁡2(4x)+1)(2cot⁡2(4x)+1)atan⁡2(2x)−6(cot⁡2(4x)+1)cot⁡(4x)atan⁡(2x)4x2+1−(2xatan⁡(2x)−1)cot⁡2(4x)(4x2+1)2)cot⁡(4x)atan⁡(2x)24 \left(4 \left(\cot^{2}{\left(4 x \right)} + 1\right) \left(2 \cot^{2}{\left(4 x \right)} + 1\right) \operatorname{atan}^{2}{\left(2 x \right)} - \frac{6 \left(\cot^{2}{\left(4 x \right)} + 1\right) \cot{\left(4 x \right)} \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{\left(2 x \operatorname{atan}{\left(2 x \right)} - 1\right) \cot^{2}{\left(4 x \right)}}{\left(4 x^{2} + 1\right)^{2}}\right) \cot{\left(4 x \right)} \operatorname{atan}{\left(2 x \right)}
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Tercera derivada [src] 
   /          /                                             2     2     \                                                                                                                                                                                                                       \
   |   3      |   1           2        12*x*atan(2*x)   16*x *atan (2*x)|                                                                                                                                                                                                                       |
   |cot (4*x)*|-------- - atan (2*x) - -------------- + ----------------|                                                                                                                                                                                                                       |
   |          |       2                          2                 2    |                                /               2                                            \         2      /       2     \                                         2      /       2     \ /         2     \         |
   |          \1 + 4*x                    1 + 4*x           1 + 4*x     /         3      /       2     \ |/       2     \         4             2      /       2     \|   18*cot (4*x)*\1 + cot (4*x)/*(-1 + 2*x*atan(2*x))*atan(2*x)   36*atan (2*x)*\1 + cot (4*x)/*\1 + 2*cot (4*x)/*cot(4*x)|
48*|--------------------------------------------------------------------- - 8*atan (2*x)*\1 + cot (4*x)/*\\1 + cot (4*x)/  + 2*cot (4*x) + 7*cot (4*x)*\1 + cot (4*x)// + ----------------------------------------------------------- + --------------------------------------------------------|
   |                                       2                                                                                                                                                                2                                                          2                        |
   |                             /       2\                                                                                                                                                       /       2\                                                    1 + 4*x                         |
   \                             \1 + 4*x /                                                                                                                                                       \1 + 4*x /                                                                                    /
48(−8(cot⁡2(4x)+1)((cot⁡2(4x)+1)2+7(cot⁡2(4x)+1)cot⁡2(4x)+2cot⁡4(4x))atan⁡3(2x)+36(cot⁡2(4x)+1)(2cot⁡2(4x)+1)cot⁡(4x)atan⁡2(2x)4x2+1+18(2xatan⁡(2x)−1)(cot⁡2(4x)+1)cot⁡2(4x)atan⁡(2x)(4x2+1)2+(16x2atan⁡2(2x)4x2+1−12xatan⁡(2x)4x2+1−atan⁡2(2x)+14x2+1)cot⁡3(4x)(4x2+1)2)48 \left(- 8 \left(\cot^{2}{\left(4 x \right)} + 1\right) \left(\left(\cot^{2}{\left(4 x \right)} + 1\right)^{2} + 7 \left(\cot^{2}{\left(4 x \right)} + 1\right) \cot^{2}{\left(4 x \right)} + 2 \cot^{4}{\left(4 x \right)}\right) \operatorname{atan}^{3}{\left(2 x \right)} + \frac{36 \left(\cot^{2}{\left(4 x \right)} + 1\right) \left(2 \cot^{2}{\left(4 x \right)} + 1\right) \cot{\left(4 x \right)} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} + \frac{18 \left(2 x \operatorname{atan}{\left(2 x \right)} - 1\right) \left(\cot^{2}{\left(4 x \right)} + 1\right) \cot^{2}{\left(4 x \right)} \operatorname{atan}{\left(2 x \right)}}{\left(4 x^{2} + 1\right)^{2}} + \frac{\left(\frac{16 x^{2} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{12 x \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} - \operatorname{atan}^{2}{\left(2 x \right)} + \frac{1}{4 x^{2} + 1}\right) \cot^{3}{\left(4 x \right)}}{\left(4 x^{2} + 1\right)^{2}}\right)
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Gráfico
Derivada de y=ctg^3*(4x)*arctg*(2x)^3
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