Mathc initiation/a0095

Sommaire

Calculons la dérivée :

          y    = asech(x)                             *
        
     sech(y)   = sech(asech(x))
    
     sech(y)   = x    
    
    (sech(y))' = (x)'  
       

      - sech(y) tanh(y)  dy/dx = 1
    
    
               dy/dx =  1/(- sech(y) tanh(y)) 
            
               dy/dx = -1/(  sech(y) tanh(y))       
                                                    *  y = asech(x)  
                                                                                                               
       d(asech(x))/dx = -1/(  sech(asech(x)) tanh(asech(x)))
       
       d(asech(x))/dx = -1/(             x   tanh(asech(x)))
              
                                               ***  tanh(asech(x)) = sqrt(1-x**2)   ***  
                                               
       d(asech(x))/dx = -1/(             x   sqrt(1-x**2))                                               
                                                 
          (asech(x))' =  -1/(x sqrt(1-x**2))

 *** tanh(asech(x)) = sqrt(1-x**2) ***