Mathc initiation/a0082

Sommaire

Calculons la dérivée :

        y = acot(x)                                        (*)
   
   cot(y) = cot(acot(x))
   
   
   cot(y) = x                                              (**)
   
   
   (cot(y))' = (x)'      
   
   -csc**2(y) dy/dx = 1
   
                                     
   dy/dx = -1/csc**2(y)               csc**2(x) - cot**2(x) = 1
                                      csc**2(x) = cot**2(x) + 1 

   dy/dx = -1/(cot**2(y) + 1)         
                                        cot(y) = x          (**)
   dy/dx = -1/(x**2 + 1)
   
                                             y = acot(x)    (*)
   d(acot(x))/dx = -1/(x**2 + 1)    
   
   
      (acot(x))' = -1/(x**2 + 1)