Mathc initiation/a0093

Sommaire

Calculons la dérivée :

        y = atanh(x)                                        (*)
   
   tanh(y) = tanh(atanh(x))
   
   
   tanh(y) = x                                              (**)
   
   
   (tanh(y))' = (x)'      
   
   sech**2(y) dy/dx = 1
   
                                     
   dy/dx = 1/sech**2(y)               sech**2(x) + tanh**2(x) = 1
                                      sech**2(x) = 1 - tanh**2(x)  

   dy/dx = 1/(1 - tanh**2(y))         
                                         tanh(y) = x          (**)
   dy/dx = 1/(1 - x**2)
   
                                               y = atanh(x)    (*)
   d(atanh(x))/dx = 1/(1 - x**2)    
   
   
      (atanh(x))' = 1/(1 - x**2)