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y=x*arctg^2(sin2x)
Derivada de la función/ ctg^2/ sin2x/ arctg/ y=x*arctg^2(sin2x)

Derivada de y=x*arctg^2(sin2x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
      2          
x*atan (sin(2*x))
xatan⁡2(sin⁡(2x))x \operatorname{atan}^{2}{\left(\sin{\left(2 x \right)} \right)} 
x*atan(sin(2*x))^2
Gráfica
02468-8-6-4-2-1010-2525
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    2             4*x*atan(sin(2*x))*cos(2*x)
atan (sin(2*x)) + ---------------------------
                                2            
                         1 + sin (2*x)
4xcos⁡(2x)atan⁡(sin⁡(2x))sin⁡2(2x)+1+atan⁡2(sin⁡(2x))\frac{4 x \cos{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)}}{\sin^{2}{\left(2 x \right)} + 1} + \operatorname{atan}^{2}{\left(\sin{\left(2 x \right)} \right)}
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Segunda derivada [src] 
  /                            /                               2               2                             \\
  |                            |                            cos (2*x)     2*cos (2*x)*atan(sin(2*x))*sin(2*x)||
8*|atan(sin(2*x))*cos(2*x) - x*|atan(sin(2*x))*sin(2*x) - ------------- + -----------------------------------||
  |                            |                                 2                          2                ||
  \                            \                          1 + sin (2*x)              1 + sin (2*x)           //
---------------------------------------------------------------------------------------------------------------
                                                        2                                                      
                                                 1 + sin (2*x)
8(−x(sin⁡(2x)atan⁡(sin⁡(2x))+2sin⁡(2x)cos⁡2(2x)atan⁡(sin⁡(2x))sin⁡2(2x)+1−cos⁡2(2x)sin⁡2(2x)+1)+cos⁡(2x)atan⁡(sin⁡(2x)))sin⁡2(2x)+1\frac{8 \left(- x \left(\sin{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)} + \frac{2 \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)}}{\sin^{2}{\left(2 x \right)} + 1} - \frac{\cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)} + 1}\right) + \cos{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)}\right)}{\sin^{2}{\left(2 x \right)} + 1}
Simplificar
3-я производная [src] 
   /        2                                         /                     2                            2                            2                      2         2                                     \                 2                             \
   |   3*cos (2*x)                                    |  3*sin(2*x)    6*sin (2*x)*atan(sin(2*x))   2*cos (2*x)*atan(sin(2*x))   6*cos (2*x)*sin(2*x)   8*cos (2*x)*sin (2*x)*atan(sin(2*x))                 |            6*cos (2*x)*atan(sin(2*x))*sin(2*x)|
-8*|- ------------- + 3*atan(sin(2*x))*sin(2*x) + 2*x*|------------- - -------------------------- + -------------------------- + -------------------- - ------------------------------------ + atan(sin(2*x))|*cos(2*x) + -----------------------------------|
   |         2                                        |       2                     2                            2                                2                              2                           |                              2                |
   |  1 + sin (2*x)                                   |1 + sin (2*x)         1 + sin (2*x)                1 + sin (2*x)            /       2     \                /       2     \                            |                       1 + sin (2*x)           |
   \                                                  \                                                                            \1 + sin (2*x)/                \1 + sin (2*x)/                            /                                               /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                               2                                                                                                                              
                                                                                                                        1 + sin (2*x)
−8(2x(atan⁡(sin⁡(2x))−6sin⁡2(2x)atan⁡(sin⁡(2x))sin⁡2(2x)+1+3sin⁡(2x)sin⁡2(2x)+1+2cos⁡2(2x)atan⁡(sin⁡(2x))sin⁡2(2x)+1−8sin⁡2(2x)cos⁡2(2x)atan⁡(sin⁡(2x))(sin⁡2(2x)+1)2+6sin⁡(2x)cos⁡2(2x)(sin⁡2(2x)+1)2)cos⁡(2x)+3sin⁡(2x)atan⁡(sin⁡(2x))+6sin⁡(2x)cos⁡2(2x)atan⁡(sin⁡(2x))sin⁡2(2x)+1−3cos⁡2(2x)sin⁡2(2x)+1)sin⁡2(2x)+1- \frac{8 \left(2 x \left(\operatorname{atan}{\left(\sin{\left(2 x \right)} \right)} - \frac{6 \sin^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)}}{\sin^{2}{\left(2 x \right)} + 1} + \frac{3 \sin{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)} + 1} + \frac{2 \cos^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)}}{\sin^{2}{\left(2 x \right)} + 1} - \frac{8 \sin^{2}{\left(2 x \right)} \cos^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)}}{\left(\sin^{2}{\left(2 x \right)} + 1\right)^{2}} + \frac{6 \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin^{2}{\left(2 x \right)} + 1\right)^{2}}\right) \cos{\left(2 x \right)} + 3 \sin{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)} + \frac{6 \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)}}{\sin^{2}{\left(2 x \right)} + 1} - \frac{3 \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)} + 1}\right)}{\sin^{2}{\left(2 x \right)} + 1}
Simplificar
Tercera derivada [src] 
   /        2                                         /                     2                            2                            2                      2         2                                     \                 2                             \
   |   3*cos (2*x)                                    |  3*sin(2*x)    6*sin (2*x)*atan(sin(2*x))   2*cos (2*x)*atan(sin(2*x))   6*cos (2*x)*sin(2*x)   8*cos (2*x)*sin (2*x)*atan(sin(2*x))                 |            6*cos (2*x)*atan(sin(2*x))*sin(2*x)|
-8*|- ------------- + 3*atan(sin(2*x))*sin(2*x) + 2*x*|------------- - -------------------------- + -------------------------- + -------------------- - ------------------------------------ + atan(sin(2*x))|*cos(2*x) + -----------------------------------|
   |         2                                        |       2                     2                            2                                2                              2                           |                              2                |
   |  1 + sin (2*x)                                   |1 + sin (2*x)         1 + sin (2*x)                1 + sin (2*x)            /       2     \                /       2     \                            |                       1 + sin (2*x)           |
   \                                                  \                                                                            \1 + sin (2*x)/                \1 + sin (2*x)/                            /                                               /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                               2                                                                                                                              
                                                                                                                        1 + sin (2*x)
−8(2x(atan⁡(sin⁡(2x))−6sin⁡2(2x)atan⁡(sin⁡(2x))sin⁡2(2x)+1+3sin⁡(2x)sin⁡2(2x)+1+2cos⁡2(2x)atan⁡(sin⁡(2x))sin⁡2(2x)+1−8sin⁡2(2x)cos⁡2(2x)atan⁡(sin⁡(2x))(sin⁡2(2x)+1)2+6sin⁡(2x)cos⁡2(2x)(sin⁡2(2x)+1)2)cos⁡(2x)+3sin⁡(2x)atan⁡(sin⁡(2x))+6sin⁡(2x)cos⁡2(2x)atan⁡(sin⁡(2x))sin⁡2(2x)+1−3cos⁡2(2x)sin⁡2(2x)+1)sin⁡2(2x)+1- \frac{8 \left(2 x \left(\operatorname{atan}{\left(\sin{\left(2 x \right)} \right)} - \frac{6 \sin^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)}}{\sin^{2}{\left(2 x \right)} + 1} + \frac{3 \sin{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)} + 1} + \frac{2 \cos^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)}}{\sin^{2}{\left(2 x \right)} + 1} - \frac{8 \sin^{2}{\left(2 x \right)} \cos^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)}}{\left(\sin^{2}{\left(2 x \right)} + 1\right)^{2}} + \frac{6 \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin^{2}{\left(2 x \right)} + 1\right)^{2}}\right) \cos{\left(2 x \right)} + 3 \sin{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)} + \frac{6 \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)}}{\sin^{2}{\left(2 x \right)} + 1} - \frac{3 \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)} + 1}\right)}{\sin^{2}{\left(2 x \right)} + 1}
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Gráfico
Derivada de y=x*arctg^2(sin2x)
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