Mathc initiation/a0081

Sommaire

Calculons la dérivée :

        y = atan(x)                                        (*)
   
   tan(y) = tan(atan(x))
   
   
   tan(y) = x                                              (**)
   
   
   (tan(y))' = (x)'      
   
   sec**2(y) dy/dx = 1
   
                                     
   dy/dx = 1/sec**2(y)               sec**2(x) - tan**2(x) = 1
                                     sec**2(x) = tan**2(x) + 1 

   dy/dx = 1/(tan**2(y) + 1)         
                                        tan(y) = x          (**)
   dy/dx = 1/(x**2 + 1)
   
                                             y = atan(x)    (*)
   d(atan(x))/dx = 1/(x**2 + 1)    
   
   
      (atan(x))' = 1/(x**2 + 1)