Sr Examen

Otras calculadoras

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

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

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    /   /1 \\
atan|sin|--||
    |   | 2||
    \   \x //
atan⁡(sin⁡(1x2))\operatorname{atan}{\left(\sin{\left(\frac{1}{x^{2}} \right)} \right)} 
atan(sin(1/(x^2)))
Gráfica
02468-8-6-4-2-1010-25002500
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
          /1 \   
    -2*cos|--|   
          | 2|   
          \x /   
-----------------
 3 /       2/1 \\
x *|1 + sin |--||
   |        | 2||
   \        \x //
−2cos⁡(1x2)x3(sin⁡2(1x2)+1)- \frac{2 \cos{\left(\frac{1}{x^{2}} \right)}}{x^{3} \left(\sin^{2}{\left(\frac{1}{x^{2}} \right)} + 1\right)}
Simplificar
Segunda derivada [src] 
  /                 /1 \        2/1 \    /1 \\
  |            2*sin|--|   4*cos |--|*sin|--||
  |                 | 2|         | 2|    | 2||
  |     /1 \        \x /         \x /    \x /|
2*|3*cos|--| - --------- - ------------------|
  |     | 2|        2       2 /       2/1 \\ |
  |     \x /       x       x *|1 + sin |--|| |
  |                           |        | 2|| |
  \                           \        \x // /
----------------------------------------------
               4 /       2/1 \\               
              x *|1 + sin |--||               
                 |        | 2||               
                 \        \x //
2(3cos⁡(1x2)−2sin⁡(1x2)x2−4sin⁡(1x2)cos⁡2(1x2)x2(sin⁡2(1x2)+1))x4(sin⁡2(1x2)+1)\frac{2 \left(3 \cos{\left(\frac{1}{x^{2}} \right)} - \frac{2 \sin{\left(\frac{1}{x^{2}} \right)}}{x^{2}} - \frac{4 \sin{\left(\frac{1}{x^{2}} \right)} \cos^{2}{\left(\frac{1}{x^{2}} \right)}}{x^{2} \left(\sin^{2}{\left(\frac{1}{x^{2}} \right)} + 1\right)}\right)}{x^{4} \left(\sin^{2}{\left(\frac{1}{x^{2}} \right)} + 1\right)}
Simplificar
Tercera derivada [src] 
  /                   /1 \        /1 \            3/1 \            3/1 \    2/1 \         2/1 \    /1 \         2/1 \    /1 \\
  |              2*cos|--|   9*sin|--|       4*cos |--|      16*cos |--|*sin |--|   12*sin |--|*cos|--|   18*cos |--|*sin|--||
  |                   | 2|        | 2|             | 2|             | 2|     | 2|          | 2|    | 2|          | 2|    | 2||
  |       /1 \        \x /        \x /             \x /             \x /     \x /          \x /    \x /          \x /    \x /|
4*|- 6*cos|--| + --------- + --------- + ----------------- - -------------------- - ------------------- + -------------------|
  |       | 2|        4           2       4 /       2/1 \\                     2      4 /       2/1 \\      2 /       2/1 \\ |
  |       \x /       x           x       x *|1 + sin |--||     4 /       2/1 \\      x *|1 + sin |--||     x *|1 + sin |--|| |
  |                                         |        | 2||    x *|1 + sin |--||         |        | 2||        |        | 2|| |
  |                                         \        \x //       |        | 2||         \        \x //        \        \x // |
  \                                                              \        \x //                                              /
------------------------------------------------------------------------------------------------------------------------------
                                                       5 /       2/1 \\                                                       
                                                      x *|1 + sin |--||                                                       
                                                         |        | 2||                                                       
                                                         \        \x //
4(−6cos⁡(1x2)+9sin⁡(1x2)x2+18sin⁡(1x2)cos⁡2(1x2)x2(sin⁡2(1x2)+1)+2cos⁡(1x2)x4−12sin⁡2(1x2)cos⁡(1x2)x4(sin⁡2(1x2)+1)+4cos⁡3(1x2)x4(sin⁡2(1x2)+1)−16sin⁡2(1x2)cos⁡3(1x2)x4(sin⁡2(1x2)+1)2)x5(sin⁡2(1x2)+1)\frac{4 \left(- 6 \cos{\left(\frac{1}{x^{2}} \right)} + \frac{9 \sin{\left(\frac{1}{x^{2}} \right)}}{x^{2}} + \frac{18 \sin{\left(\frac{1}{x^{2}} \right)} \cos^{2}{\left(\frac{1}{x^{2}} \right)}}{x^{2} \left(\sin^{2}{\left(\frac{1}{x^{2}} \right)} + 1\right)} + \frac{2 \cos{\left(\frac{1}{x^{2}} \right)}}{x^{4}} - \frac{12 \sin^{2}{\left(\frac{1}{x^{2}} \right)} \cos{\left(\frac{1}{x^{2}} \right)}}{x^{4} \left(\sin^{2}{\left(\frac{1}{x^{2}} \right)} + 1\right)} + \frac{4 \cos^{3}{\left(\frac{1}{x^{2}} \right)}}{x^{4} \left(\sin^{2}{\left(\frac{1}{x^{2}} \right)} + 1\right)} - \frac{16 \sin^{2}{\left(\frac{1}{x^{2}} \right)} \cos^{3}{\left(\frac{1}{x^{2}} \right)}}{x^{4} \left(\sin^{2}{\left(\frac{1}{x^{2}} \right)} + 1\right)^{2}}\right)}{x^{5} \left(\sin^{2}{\left(\frac{1}{x^{2}} \right)} + 1\right)}
Simplificar
Gráfico
Derivada de y=arctg(sin(1/x^2))
    © Sr Examen – Калькулятор