Mathc initiation/a0084

Sommaire

Calculons la dérivée :

         y    = acsc(x)                             *
        
     csc(y)   = csc(acsc(x))
    
     csc(y)   = x                                   *
    
    (csc(y))' = (x)'  
       

 (-csc(y) cot(y)) dy/dx = 1

    
                 dy/dx =  1/(-csc(y) cot(y)) 
                       = -1/( csc(y) cot(y)) 
                                                    * csc(y) = x
                                                    *     y  = acsc(x)     
       
       d(acsc(x))/dx =  -1/(x cot(acsc(x))) 
                                               *** cot(acsc(x)) = sqrt(x**2-1) ***    
          (acsc(x))' =  -1/(x sqrt(x**2-1))

 *** cot(acsc(x)) = sqrt(x**2-1) ***