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y=arctg^2(cos3x)
Derivada de la función/ cos3x/ ctg^2/ arctg/ y=arctg^2(cos3x)

Derivada de y=arctg^2(cos3x)

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

Ha introducido [src] 
    2          
atan (cos(3*x))
atan⁡2(cos⁡(3x))\operatorname{atan}^{2}{\left(\cos{\left(3 x \right)} \right)} 
atan(cos(3*x))^2
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
-6*atan(cos(3*x))*sin(3*x)
--------------------------
             2            
      1 + cos (3*x)
−6sin⁡(3x)atan⁡(cos⁡(3x))cos⁡2(3x)+1- \frac{6 \sin{\left(3 x \right)} \operatorname{atan}{\left(\cos{\left(3 x \right)} \right)}}{\cos^{2}{\left(3 x \right)} + 1}
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Segunda derivada [src] 
   /     2                                         2                             \
   |  sin (3*x)                               2*sin (3*x)*atan(cos(3*x))*cos(3*x)|
18*|------------- - atan(cos(3*x))*cos(3*x) - -----------------------------------|
   |       2                                                    2                |
   \1 + cos (3*x)                                        1 + cos (3*x)           /
----------------------------------------------------------------------------------
                                         2                                        
                                  1 + cos (3*x)
18(−cos⁡(3x)atan⁡(cos⁡(3x))−2sin⁡2(3x)cos⁡(3x)atan⁡(cos⁡(3x))cos⁡2(3x)+1+sin⁡2(3x)cos⁡2(3x)+1)cos⁡2(3x)+1\frac{18 \left(- \cos{\left(3 x \right)} \operatorname{atan}{\left(\cos{\left(3 x \right)} \right)} - \frac{2 \sin^{2}{\left(3 x \right)} \cos{\left(3 x \right)} \operatorname{atan}{\left(\cos{\left(3 x \right)} \right)}}{\cos^{2}{\left(3 x \right)} + 1} + \frac{\sin^{2}{\left(3 x \right)}}{\cos^{2}{\left(3 x \right)} + 1}\right)}{\cos^{2}{\left(3 x \right)} + 1}
Simplificar
Tercera derivada [src] 
   /                     2                            2                            2                      2         2                                     \         
   |  3*cos(3*x)    6*cos (3*x)*atan(cos(3*x))   2*sin (3*x)*atan(cos(3*x))   6*sin (3*x)*cos(3*x)   8*cos (3*x)*sin (3*x)*atan(cos(3*x))                 |         
54*|------------- - -------------------------- + -------------------------- + -------------------- - ------------------------------------ + atan(cos(3*x))|*sin(3*x)
   |       2                     2                            2                                2                              2                           |         
   |1 + cos (3*x)         1 + cos (3*x)                1 + cos (3*x)            /       2     \                /       2     \                            |         
   \                                                                            \1 + cos (3*x)/                \1 + cos (3*x)/                            /         
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                                                                                  2                                                                                 
                                                                           1 + cos (3*x)
54(atan⁡(cos⁡(3x))+2sin⁡2(3x)atan⁡(cos⁡(3x))cos⁡2(3x)+1−6cos⁡2(3x)atan⁡(cos⁡(3x))cos⁡2(3x)+1+3cos⁡(3x)cos⁡2(3x)+1−8sin⁡2(3x)cos⁡2(3x)atan⁡(cos⁡(3x))(cos⁡2(3x)+1)2+6sin⁡2(3x)cos⁡(3x)(cos⁡2(3x)+1)2)sin⁡(3x)cos⁡2(3x)+1\frac{54 \left(\operatorname{atan}{\left(\cos{\left(3 x \right)} \right)} + \frac{2 \sin^{2}{\left(3 x \right)} \operatorname{atan}{\left(\cos{\left(3 x \right)} \right)}}{\cos^{2}{\left(3 x \right)} + 1} - \frac{6 \cos^{2}{\left(3 x \right)} \operatorname{atan}{\left(\cos{\left(3 x \right)} \right)}}{\cos^{2}{\left(3 x \right)} + 1} + \frac{3 \cos{\left(3 x \right)}}{\cos^{2}{\left(3 x \right)} + 1} - \frac{8 \sin^{2}{\left(3 x \right)} \cos^{2}{\left(3 x \right)} \operatorname{atan}{\left(\cos{\left(3 x \right)} \right)}}{\left(\cos^{2}{\left(3 x \right)} + 1\right)^{2}} + \frac{6 \sin^{2}{\left(3 x \right)} \cos{\left(3 x \right)}}{\left(\cos^{2}{\left(3 x \right)} + 1\right)^{2}}\right) \sin{\left(3 x \right)}}{\cos^{2}{\left(3 x \right)} + 1}
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Gráfico
Derivada de y=arctg^2(cos3x)
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