I don't know whether you've ever found derivatives of functions by first principles, but if you did then you'd see that your order is correct.
The idea is to take two points on a curve, joining them up with a line. If you keep one point fixed, moving the other one closer to it, then as you move them closer and closer to each other, you can obtain the limit of the line joining the two points. Then when the seperation tends to zero, the gradient of your line tends to the gradient of the curve at that point.
Indeed, the derivative is defined using limits:
dy/dx = limh->0 [ (f(x+h) - f(x))/h ]
I'm pretty certain integration came afterwards, using the same kind of principles. Could be wrong about that though.
Hope this helps.