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y=arctg^2(sh2x)
Derivada de la función/ ctg^2/ arctg/ y=arctg^2(sh2x)

Derivada de y=arctg^2(sh2x)

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

Ha introducido [src] 
    2           
atan (sinh(2*x))
atan⁡2(sinh⁡(2x))\operatorname{atan}^{2}{\left(\sinh{\left(2 x \right)} \right)} 
atan(sinh(2*x))^2
Gráfica
02468-8-6-4-2-10105-5
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Trazar el gráfico f'(x)
Primera derivada [src] 
4*atan(sinh(2*x))*cosh(2*x)
---------------------------
               2           
       1 + sinh (2*x)
4cosh⁡(2x)atan⁡(sinh⁡(2x))sinh⁡2(2x)+1\frac{4 \cosh{\left(2 x \right)} \operatorname{atan}{\left(\sinh{\left(2 x \right)} \right)}}{\sinh^{2}{\left(2 x \right)} + 1}
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Segunda derivada [src] 
  /      2                                            2                               \
  |  cosh (2*x)                                 2*cosh (2*x)*atan(sinh(2*x))*sinh(2*x)|
8*|-------------- + atan(sinh(2*x))*sinh(2*x) - --------------------------------------|
  |        2                                                        2                 |
  \1 + sinh (2*x)                                           1 + sinh (2*x)            /
---------------------------------------------------------------------------------------
                                             2                                         
                                     1 + sinh (2*x)
8(sinh⁡(2x)atan⁡(sinh⁡(2x))−2sinh⁡(2x)cosh⁡2(2x)atan⁡(sinh⁡(2x))sinh⁡2(2x)+1+cosh⁡2(2x)sinh⁡2(2x)+1)sinh⁡2(2x)+1\frac{8 \left(\sinh{\left(2 x \right)} \operatorname{atan}{\left(\sinh{\left(2 x \right)} \right)} - \frac{2 \sinh{\left(2 x \right)} \cosh^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sinh{\left(2 x \right)} \right)}}{\sinh^{2}{\left(2 x \right)} + 1} + \frac{\cosh^{2}{\left(2 x \right)}}{\sinh^{2}{\left(2 x \right)} + 1}\right)}{\sinh^{2}{\left(2 x \right)} + 1}
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Tercera derivada [src] 
   /                       2                              2                        2                              2          2                                       \          
   | 3*sinh(2*x)     6*sinh (2*x)*atan(sinh(2*x))   6*cosh (2*x)*sinh(2*x)   2*cosh (2*x)*atan(sinh(2*x))   8*cosh (2*x)*sinh (2*x)*atan(sinh(2*x))                  |          
16*|-------------- - ---------------------------- - ---------------------- - ---------------------------- + --------------------------------------- + atan(sinh(2*x))|*cosh(2*x)
   |        2                       2                                 2                     2                                          2                             |          
   |1 + sinh (2*x)          1 + sinh (2*x)            /        2     \              1 + sinh (2*x)                     /        2     \                              |          
   \                                                  \1 + sinh (2*x)/                                                 \1 + sinh (2*x)/                              /          
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                         2                                                                                      
                                                                                 1 + sinh (2*x)
16(atan⁡(sinh⁡(2x))−6sinh⁡2(2x)atan⁡(sinh⁡(2x))sinh⁡2(2x)+1+3sinh⁡(2x)sinh⁡2(2x)+1−2cosh⁡2(2x)atan⁡(sinh⁡(2x))sinh⁡2(2x)+1+8sinh⁡2(2x)cosh⁡2(2x)atan⁡(sinh⁡(2x))(sinh⁡2(2x)+1)2−6sinh⁡(2x)cosh⁡2(2x)(sinh⁡2(2x)+1)2)cosh⁡(2x)sinh⁡2(2x)+1\frac{16 \left(\operatorname{atan}{\left(\sinh{\left(2 x \right)} \right)} - \frac{6 \sinh^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sinh{\left(2 x \right)} \right)}}{\sinh^{2}{\left(2 x \right)} + 1} + \frac{3 \sinh{\left(2 x \right)}}{\sinh^{2}{\left(2 x \right)} + 1} - \frac{2 \cosh^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sinh{\left(2 x \right)} \right)}}{\sinh^{2}{\left(2 x \right)} + 1} + \frac{8 \sinh^{2}{\left(2 x \right)} \cosh^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sinh{\left(2 x \right)} \right)}}{\left(\sinh^{2}{\left(2 x \right)} + 1\right)^{2}} - \frac{6 \sinh{\left(2 x \right)} \cosh^{2}{\left(2 x \right)}}{\left(\sinh^{2}{\left(2 x \right)} + 1\right)^{2}}\right) \cosh{\left(2 x \right)}}{\sinh^{2}{\left(2 x \right)} + 1}
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Gráfico
Derivada de y=arctg^2(sh2x)
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