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

Derivada de arctg^2(1/x)

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

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Solución

Ha introducido [src] 
    2/1\
atan |-|
     \x/
atan⁡2(1x)\operatorname{atan}^{2}{\left(\frac{1}{x} \right)} 
atan(1/x)^2
Gráfica
02468-8-6-4-2-10105-5
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Trazar el gráfico f'(x)
Primera derivada [src] 
        /1\
 -2*atan|-|
        \x/
-----------
 2 /    1 \
x *|1 + --|
   |     2|
   \    x /
−2atan⁡(1x)x2(1+1x2)- \frac{2 \operatorname{atan}{\left(\frac{1}{x} \right)}}{x^{2} \left(1 + \frac{1}{x^{2}}\right)}
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Segunda derivada [src] 
  /                                /1\ \
  |                          2*atan|-| |
  |      /1\       1               \x/ |
2*|2*atan|-| + ---------- - -----------|
  |      \x/     /    1 \    2 /    1 \|
  |            x*|1 + --|   x *|1 + --||
  |              |     2|      |     2||
  \              \    x /      \    x //
----------------------------------------
               3 /    1 \               
              x *|1 + --|               
                 |     2|               
                 \    x /
2(2atan⁡(1x)+1x(1+1x2)−2atan⁡(1x)x2(1+1x2))x3(1+1x2)\frac{2 \left(2 \operatorname{atan}{\left(\frac{1}{x} \right)} + \frac{1}{x \left(1 + \frac{1}{x^{2}}\right)} - \frac{2 \operatorname{atan}{\left(\frac{1}{x} \right)}}{x^{2} \left(1 + \frac{1}{x^{2}}\right)}\right)}{x^{3} \left(1 + \frac{1}{x^{2}}\right)}
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Tercera derivada [src] 
  /                                                 /1\            /1\ \
  |                                           4*atan|-|      7*atan|-| |
  |        /1\       3             3                \x/            \x/ |
4*|- 3*atan|-| - ---------- + ------------ - ------------ + -----------|
  |        \x/     /    1 \              2              2    2 /    1 \|
  |              x*|1 + --|    3 /    1 \     4 /    1 \    x *|1 + --||
  |                |     2|   x *|1 + --|    x *|1 + --|       |     2||
  |                \    x /      |     2|       |     2|       \    x /|
  \                              \    x /       \    x /               /
------------------------------------------------------------------------
                               4 /    1 \                               
                              x *|1 + --|                               
                                 |     2|                               
                                 \    x /
4(−3atan⁡(1x)−3x(1+1x2)+7atan⁡(1x)x2(1+1x2)+3x3(1+1x2)2−4atan⁡(1x)x4(1+1x2)2)x4(1+1x2)\frac{4 \left(- 3 \operatorname{atan}{\left(\frac{1}{x} \right)} - \frac{3}{x \left(1 + \frac{1}{x^{2}}\right)} + \frac{7 \operatorname{atan}{\left(\frac{1}{x} \right)}}{x^{2} \left(1 + \frac{1}{x^{2}}\right)} + \frac{3}{x^{3} \left(1 + \frac{1}{x^{2}}\right)^{2}} - \frac{4 \operatorname{atan}{\left(\frac{1}{x} \right)}}{x^{4} \left(1 + \frac{1}{x^{2}}\right)^{2}}\right)}{x^{4} \left(1 + \frac{1}{x^{2}}\right)}
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Gráfico
Derivada de arctg^2(1/x)
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