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y=arctg^2(1/x)

Derivada de y=arctg^2(1/x)

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

Gráfico:

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Solución

Ha introducido [src]
    2/1\
atan |-|
     \x/
$$\operatorname{atan}^{2}{\left(\frac{1}{x} \right)}$$
atan(1/x)^2
Gráfica
Primera derivada [src]
        /1\
 -2*atan|-|
        \x/
-----------
 2 /    1 \
x *|1 + --|
   |     2|
   \    x /
$$- \frac{2 \operatorname{atan}{\left(\frac{1}{x} \right)}}{x^{2} \left(1 + \frac{1}{x^{2}}\right)}$$
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 /               
$$\frac{2 \left(2 \operatorname{atan}{\left(\frac{1}{x} \right)} + \frac{1}{x \left(1 + \frac{1}{x^{2}}\right)} - \frac{2 \operatorname{atan}{\left(\frac{1}{x} \right)}}{x^{2} \left(1 + \frac{1}{x^{2}}\right)}\right)}{x^{3} \left(1 + \frac{1}{x^{2}}\right)}$$
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 /                               
$$\frac{4 \left(- 3 \operatorname{atan}{\left(\frac{1}{x} \right)} - \frac{3}{x \left(1 + \frac{1}{x^{2}}\right)} + \frac{7 \operatorname{atan}{\left(\frac{1}{x} \right)}}{x^{2} \left(1 + \frac{1}{x^{2}}\right)} + \frac{3}{x^{3} \left(1 + \frac{1}{x^{2}}\right)^{2}} - \frac{4 \operatorname{atan}{\left(\frac{1}{x} \right)}}{x^{4} \left(1 + \frac{1}{x^{2}}\right)^{2}}\right)}{x^{4} \left(1 + \frac{1}{x^{2}}\right)}$$
Gráfico
Derivada de y=arctg^2(1/x)