f(x) = (3/4x -6)e^0,5x-2   + 5

on rappelle que :

[ u(x) v(x) ]' = u'(x) v(x) + u(x) v'(x)

[e^u(x)]' = u'(x)e^u(x)

on pose u(x) = 3/4x - 6           u'(x) = 3/4

             v(x) = e^0,5x-2           v'(x) = 0,5e^0,5x-2

f'x) = 3/4 e^0,5x-2 + (3/4x - 6 )0,5e^0,5x-2

    =  3/4 e^0,5x-2 - 6(0,5e^0,5x-2) + (3/4)x(0,5e^0,5x-2)

   = (3/4) e^0,5x-2  - 3e^0,5x-2  + (3/8)xe^0,5x-2

  = (3/4 - 3) e^0,5x-2 + (3/8)xe^0,5x-2

  = (-9/4)e^0,5x-2 + (3/8)xe^0,5x-2

  = (3/8x - 9/4)e^0,5x-2