Let's differntiate:

y = 2x^2 + 2x + 4

=> dy/dx = 4x + 2

=> dy = dx(4x + 2)...........multiplied both sides by dx

when x = 1 and dx = 0.3

=> dy = 0.3(4(1) + 2)

=> dy = 1.8

when x = 1 and dx = 0.6

=> dy = 0.6(4(1) + 2)

=> dy = 3.6

the trick is that dy/dx is more than just a notation, we can treat it like a fraction and split it up, so we are able to solve for one piece of it