Here's a little song you might likeY Will Derive
(sung to the tune of "I Will Survive" by Gloria Gaynor)
Once, I was afraid of the passing time
How all my measurements would change along some crazy line
And, it was not for me to know
How fast my measurements would grow
Would they go slow?
And if at any single moment
Would they peak?
Or fall down flat?
I thought that calculators only could decipher all of that
I should have stayed awake in Calculus and got above a C
If I had known for just one second it could manage time for me
So, now rise! Make loopedy-loops!
I've got my Calc now. I've got all my dirt on you.
Weren't you that function with those crazy little lines?
You think you're big? You think you scared me out'my mind?
Oh, no, not y
Y will derive
As long as it's continuous the answer will arrive
I've got all unknowns to find, but I've got all my wits combined
Y will derive
Y will derive
Hey, hey
What's a person gotta do to find y-prime?
The instant rate of change is slope of any tangent line
You find d-x approaching zero, put it under change in y
It's undefined. But, you reduce and simplify
You've got your rate
d-y-d-x
Now, you can find all max's, mins, and where concavity inflects
What genius saw in motion more than just the distance that was there,
And realized acceleration was in feet per seconds squared?
Now decrease! Dip down in shame!
I've got my Calc now. I've got your number and your name
Weren't you that function with those curves you thought were cool?
You think you're special? You think you're better than the rules?
Oh, no, not y
Y will derive
With differential Calculus you'll never be deprived
I've got related rates to solve and I've got growth rates to evolve
Y will derive
Y will derive
Go nuts! Twist in and out!
I've got my Calc now. I know what you're about
Weren't you that function with the sinusoidal waves?
You think you're clever? 'Cause you rebel and misbehave?
Oh, no, not y
Y will derive
I'm taking that AP test and I know I'll score a 5
I've got all my time to cruise, 'cause I know all the rules to use
Y will derive
Y will derive