MODUL-MATEMATIKA-EKONOMI-2

Laboratorium Manajemen Dasar6. Diferensiasi hasil bagi fungsiJika y = u u’.v – u.v’, dimana u = g (x) dan v = h (x), maka y’ =v v 2Contoh : y = ( – )( – )u = (9x 2 – 5)u’ = 2.9x 2-1 = 18xv = (4x 3 – 6) v’ = 3.4x 3-1 = 12x 2’. – .’karena y’ = , maka: y’ = ()( – ) – ( – )( )( – ) y’ = – – ( – ) y’ = ( – )7. Diferensiasi fungsi komposisi (dalil rantai)Jika y = f (u) sedangkan u = g (x) , dengan kata lain y = f [ g (x) ], makadydx = dydu x dudxContoh 1: y = (6x 2 + 4) 2misalkan : u = 6x 2 +4 , sehingga y = u 2 = 12x = 2uMaka dydx = dydu x dudx = 2u . 12x = 2 (6x2 + 4) (12x) = 144x 3 + 96xContoh 2: y = √3x 2 + 4x – 5y = (3x 2 + 4x - 5) 1/2misalkan : u = 3x 2 + 4x -5 , sehingga y = u 1/2 = 6x + 4 = ½ u-1/2Matematika Ekonomi 2 3 Litbang ATA 13/14