Sr Examen

Otras calculadoras

y=arctg((2x-1)^1/2)*(cos(1/x))^2
Derivada de la función/ y=arctg((2x-1)^1/2)*(cos(1/x))^2

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

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    /  _________\    2/1\
atan\\/ 2*x - 1 /*cos |-|
                      \x/
cos⁡2(1x)atan⁡(2x−1)\cos^{2}{\left(\frac{1}{x} \right)} \operatorname{atan}{\left(\sqrt{2 x - 1} \right)} 
atan(sqrt(2*x - 1))*cos(1/x)^2
Gráfica
02468-8-6-4-2-101002
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
       2/1\             /  _________\    /1\    /1\
    cos |-|       2*atan\\/ 2*x - 1 /*cos|-|*sin|-|
        \x/                              \x/    \x/
--------------- + ---------------------------------
      _________                    2               
2*x*\/ 2*x - 1                    x
cos⁡2(1x)2x2x−1+2sin⁡(1x)cos⁡(1x)atan⁡(2x−1)x2\frac{\cos^{2}{\left(\frac{1}{x} \right)}}{2 x \sqrt{2 x - 1}} + \frac{2 \sin{\left(\frac{1}{x} \right)} \cos{\left(\frac{1}{x} \right)} \operatorname{atan}{\left(\sqrt{2 x - 1} \right)}}{x^{2}}
Simplificar
Segunda derivada [src] 
    /   2/1\      2/1\                  \                                                              
    |cos |-|   sin |-|                  |                                                              
    |    \x/       \x/        /1\    /1\|     /  __________\      2/1\ /1      1    \        /1\    /1\
  2*|------- - ------- + 2*cos|-|*sin|-||*atan\\/ -1 + 2*x /   cos |-|*|- + --------|   2*cos|-|*sin|-|
    \   x         x           \x/    \x//                          \x/ \x   -1 + 2*x/        \x/    \x/
- ---------------------------------------------------------- - ---------------------- + ---------------
                               2                                       __________        2   __________
                              x                                    2*\/ -1 + 2*x        x *\/ -1 + 2*x 
-------------------------------------------------------------------------------------------------------
                                                   x
−(12x−1+1x)cos⁡2(1x)22x−1−2(2sin⁡(1x)cos⁡(1x)−sin⁡2(1x)x+cos⁡2(1x)x)atan⁡(2x−1)x2+2sin⁡(1x)cos⁡(1x)x22x−1x\frac{- \frac{\left(\frac{1}{2 x - 1} + \frac{1}{x}\right) \cos^{2}{\left(\frac{1}{x} \right)}}{2 \sqrt{2 x - 1}} - \frac{2 \left(2 \sin{\left(\frac{1}{x} \right)} \cos{\left(\frac{1}{x} \right)} - \frac{\sin^{2}{\left(\frac{1}{x} \right)}}{x} + \frac{\cos^{2}{\left(\frac{1}{x} \right)}}{x}\right) \operatorname{atan}{\left(\sqrt{2 x - 1} \right)}}{x^{2}} + \frac{2 \sin{\left(\frac{1}{x} \right)} \cos{\left(\frac{1}{x} \right)}}{x^{2} \sqrt{2 x - 1}}}{x}
Simplificar
Tercera derivada [src] 
                                                                                        /       2/1\        2/1\                          /1\    /1\\                                                    
                                              /   2/1\      2/1\                  \     |  3*sin |-|   3*cos |-|                     2*cos|-|*sin|-||                                                    
   2/1\ /2         3             2      \     |cos |-|   sin |-|                  |     |        \x/         \x/        /1\    /1\        \x/    \x/|     /  __________\                                 
cos |-|*|-- + ----------- + ------------|     |    \x/       \x/        /1\    /1\|   4*|- --------- + --------- + 3*cos|-|*sin|-| - ---------------|*atan\\/ -1 + 2*x /     /1      1    \    /1\    /1\
    \x/ | 2             2   x*(-1 + 2*x)|   3*|------- - ------- + 2*cos|-|*sin|-||     |      x           x            \x/    \x/           2      |                      3*|- + --------|*cos|-|*sin|-|
        \x    (-1 + 2*x)                /     \   x         x           \x/    \x//     \                                                   x       /                        \x   -1 + 2*x/    \x/    \x/
----------------------------------------- - --------------------------------------- + ---------------------------------------------------------------------------------- - ------------------------------
                  __________                             3   __________                                                        3                                                   2   __________        
              2*\/ -1 + 2*x                             x *\/ -1 + 2*x                                                        x                                                   x *\/ -1 + 2*x         
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                    x
(3(2x−1)2+2x(2x−1)+2x2)cos⁡2(1x)22x−1−3(12x−1+1x)sin⁡(1x)cos⁡(1x)x22x−1+4(3sin⁡(1x)cos⁡(1x)−3sin⁡2(1x)x+3cos⁡2(1x)x−2sin⁡(1x)cos⁡(1x)x2)atan⁡(2x−1)x3−3(2sin⁡(1x)cos⁡(1x)−sin⁡2(1x)x+cos⁡2(1x)x)x32x−1x\frac{\frac{\left(\frac{3}{\left(2 x - 1\right)^{2}} + \frac{2}{x \left(2 x - 1\right)} + \frac{2}{x^{2}}\right) \cos^{2}{\left(\frac{1}{x} \right)}}{2 \sqrt{2 x - 1}} - \frac{3 \left(\frac{1}{2 x - 1} + \frac{1}{x}\right) \sin{\left(\frac{1}{x} \right)} \cos{\left(\frac{1}{x} \right)}}{x^{2} \sqrt{2 x - 1}} + \frac{4 \left(3 \sin{\left(\frac{1}{x} \right)} \cos{\left(\frac{1}{x} \right)} - \frac{3 \sin^{2}{\left(\frac{1}{x} \right)}}{x} + \frac{3 \cos^{2}{\left(\frac{1}{x} \right)}}{x} - \frac{2 \sin{\left(\frac{1}{x} \right)} \cos{\left(\frac{1}{x} \right)}}{x^{2}}\right) \operatorname{atan}{\left(\sqrt{2 x - 1} \right)}}{x^{3}} - \frac{3 \left(2 \sin{\left(\frac{1}{x} \right)} \cos{\left(\frac{1}{x} \right)} - \frac{\sin^{2}{\left(\frac{1}{x} \right)}}{x} + \frac{\cos^{2}{\left(\frac{1}{x} \right)}}{x}\right)}{x^{3} \sqrt{2 x - 1}}}{x}
Simplificar
Gráfico
Derivada de y=arctg((2x-1)^1/2)*(cos(1/x))^2
    © Sr Examen – Калькулятор