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е^ctg2x/arctg3x^2
Derivada de la función/ ctg2x/ arctg/ ctg3x/ е^ctg2x/arctg3x^2

Derivada de е^ctg2x/arctg3x^2

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 cot(2*x) 
E         
----------
    2     
atan (3*x)
ecot⁡(2x)atan⁡2(3x)\frac{e^{\cot{\left(2 x \right)}}}{\operatorname{atan}^{2}{\left(3 x \right)}} 
E^cot(2*x)/atan(3*x)^2
Gráfica
02468-8-6-4-2-1010-5e245e24
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
/          2     \  cot(2*x)           cot(2*x)     
\-2 - 2*cot (2*x)/*e                6*e             
---------------------------- - ---------------------
             2                 /       2\     3     
         atan (3*x)            \1 + 9*x /*atan (3*x)
(−2cot⁡2(2x)−2)ecot⁡(2x)atan⁡2(3x)−6ecot⁡(2x)(9x2+1)atan⁡3(3x)\frac{\left(- 2 \cot^{2}{\left(2 x \right)} - 2\right) e^{\cot{\left(2 x \right)}}}{\operatorname{atan}^{2}{\left(3 x \right)}} - \frac{6 e^{\cot{\left(2 x \right)}}}{\left(9 x^{2} + 1\right) \operatorname{atan}^{3}{\left(3 x \right)}}
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Segunda derivada [src] 
  /                                                                            /    1          \\          
  |                                                     /       2     \     27*|--------- + 2*x||          
  |  /       2     \ /       2                  \    12*\1 + cot (2*x)/        \atan(3*x)      /|  cot(2*x)
2*|2*\1 + cot (2*x)/*\1 + cot (2*x) + 2*cot(2*x)/ + -------------------- + ---------------------|*e        
  |                                                 /       2\                       2          |          
  |                                                 \1 + 9*x /*atan(3*x)   /       2\           |          
  \                                                                        \1 + 9*x / *atan(3*x)/          
-----------------------------------------------------------------------------------------------------------
                                                     2                                                     
                                                 atan (3*x)
2(27(2x+1atan⁡(3x))(9x2+1)2atan⁡(3x)+2(cot⁡2(2x)+1)(cot⁡2(2x)+2cot⁡(2x)+1)+12(cot⁡2(2x)+1)(9x2+1)atan⁡(3x))ecot⁡(2x)atan⁡2(3x)\frac{2 \left(\frac{27 \left(2 x + \frac{1}{\operatorname{atan}{\left(3 x \right)}}\right)}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}{\left(3 x \right)}} + 2 \left(\cot^{2}{\left(2 x \right)} + 1\right) \left(\cot^{2}{\left(2 x \right)} + 2 \cot{\left(2 x \right)} + 1\right) + \frac{12 \left(\cot^{2}{\left(2 x \right)} + 1\right)}{\left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}}\right) e^{\cot{\left(2 x \right)}}}{\operatorname{atan}^{2}{\left(3 x \right)}}
Simplificar
Tercera derivada [src] 
   /                                                                                         /                                  2                         \                                                                                         \          
   |                                                                                         |               6              36*x              27*x        |                                                                                         |          
   |                                                                                      27*|-1 + --------------------- + -------- + --------------------|                                                        /       2     \ /    1          \|          
   |                  /                   2                                           \      |     /       2\     2               2   /       2\          |      /       2     \ /       2                  \   81*\1 + cot (2*x)/*|--------- + 2*x||          
   |  /       2     \ |    /       2     \         2          /       2     \         |      \     \1 + 9*x /*atan (3*x)   1 + 9*x    \1 + 9*x /*atan(3*x)/   18*\1 + cot (2*x)/*\1 + cot (2*x) + 2*cot(2*x)/                      \atan(3*x)      /|  cot(2*x)
-4*|2*\1 + cot (2*x)/*\2 + \1 + cot (2*x)/  + 6*cot (2*x) + 6*\1 + cot (2*x)/*cot(2*x)/ + ----------------------------------------------------------------- + ----------------------------------------------- + ------------------------------------|*e        
   |                                                                                                                      2                                                 /       2\                                           2                  |          
   |                                                                                                            /       2\                                                  \1 + 9*x /*atan(3*x)                       /       2\                   |          
   \                                                                                                            \1 + 9*x / *atan(3*x)                                                                                  \1 + 9*x / *atan(3*x)        /          
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                               2                                                                                                                               
                                                                                                                           atan (3*x)
−4(81(2x+1atan⁡(3x))(cot⁡2(2x)+1)(9x2+1)2atan⁡(3x)+2(cot⁡2(2x)+1)((cot⁡2(2x)+1)2+6(cot⁡2(2x)+1)cot⁡(2x)+6cot⁡2(2x)+2)+18(cot⁡2(2x)+1)(cot⁡2(2x)+2cot⁡(2x)+1)(9x2+1)atan⁡(3x)+27(36x29x2+1+27x(9x2+1)atan⁡(3x)−1+6(9x2+1)atan⁡2(3x))(9x2+1)2atan⁡(3x))ecot⁡(2x)atan⁡2(3x)- \frac{4 \left(\frac{81 \left(2 x + \frac{1}{\operatorname{atan}{\left(3 x \right)}}\right) \left(\cot^{2}{\left(2 x \right)} + 1\right)}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}{\left(3 x \right)}} + 2 \left(\cot^{2}{\left(2 x \right)} + 1\right) \left(\left(\cot^{2}{\left(2 x \right)} + 1\right)^{2} + 6 \left(\cot^{2}{\left(2 x \right)} + 1\right) \cot{\left(2 x \right)} + 6 \cot^{2}{\left(2 x \right)} + 2\right) + \frac{18 \left(\cot^{2}{\left(2 x \right)} + 1\right) \left(\cot^{2}{\left(2 x \right)} + 2 \cot{\left(2 x \right)} + 1\right)}{\left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}} + \frac{27 \left(\frac{36 x^{2}}{9 x^{2} + 1} + \frac{27 x}{\left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}} - 1 + \frac{6}{\left(9 x^{2} + 1\right) \operatorname{atan}^{2}{\left(3 x \right)}}\right)}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}{\left(3 x \right)}}\right) e^{\cot{\left(2 x \right)}}}{\operatorname{atan}^{2}{\left(3 x \right)}}
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Gráfico
Derivada de е^ctg2x/arctg3x^2
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