The rate of change in z at (4,9) as we change x but hold y fixed is = 3/[2sqrt(3x+2y)] put x = 4 , y = 9 = 3/[2sqrt(12+18) = 3/[2sqrt(30)] The rate of change in z at (4,9) as we change y but hold x fixed is = 1/sqrt(3x+2y) put x = 4, y =9 = 1/sqrt(30)