Mathc initiation/a0094

Sommaire

Calculons la dérivée :

        y = acoth(x)                                        (*)
   
   coth(y) = coth(acoth(x))
   
   
   coth(y) = x                                              (**)
   
   
   (coth(y))' = (x)'      
   
   -csch**2(y) dy/dx = 1
   
                                     
   dy/dx =  1/(-csch**2(y))
   
   dy/dx = -1/  csch**2(y)             coth**2(x) - csch**2(x) =  1
                                                  - csch**2(x) =  1 -coth**2(x) 
                                                    csch**2(x) = -1 +coth**2(x)   
                                                    csch**2(x) = coth**2(x) - 1 
   dy/dx = -1/(coth**2(y) - 1)         
                                         coth(y) = x          (**)
   dy/dx = -1/(x**2 - 1)
   
                                               y = acoth(x)    (*)
   d(acoth(x))/dx = -1/(x**2 - 1)   
   
   
      (acoth(x))' = -1/(x**2 - 1)
      
      (acoth(x))' =  1/(1 - x**2)