I remember the day in my last year in high school, when my physics teacher looked at us with a frustrated face and asked: "So, you still didn't have derivation

I remember the day in my last year in high school, when my physics teacher looked at us with a frustrated face and asked: "So, you still didn't have derivation in math class?" We explained, that we will have it in the final month of the school year, if we are lucky. Her reaction was: "But we kinda need it already. But I should be able to teach you that in 20 minutes." And she did. And then she spent the rest of the lesson going through some old equations that she might have spent hours explaining: "Remember how long it took us to get to i.e: equation relating gass pressure and temperature? We always used that finicky helper variable. I think I even named it delta. In reality, you just derive this base form, and do a simple substitution." Ok, my memory is a bit hazy. But she went on and on, through stuff we have been ehm, deriving without calculus for hours, that took with calculus around 3-4 steps.