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
