The derivative of the sine is the cosine
And cosine’s derivative is a negative sine
To find the slope of tan you use secant’s square and
Wait, you look confused, should I go back a moment there?

Oh it’s Calculus Monday and I’m here to tell you
A bit about derivatives and what they can do.
To differentiate a function’s to talk about it’s slope
Well, rate-of-change and so a constant function we’d hope
Evaluates to zero, or this whole change thing’s a joke!

Derivatives can describe motion and show how two things relate;
With them you can optimize and even calculate
Things like the earth’s path around the sun,
Or how to build a ‘coaster that is both safe and fun!

To find the derivative of a sum you just differentiate each part;
The product of two functions? Take the prime of each to start.
Multiply by the other, and sum those pieces together!

X to the n becomes n times x to the n minus one,
While with e to the x you’re already done!
For a function of a function, say an f of g of x,
You take f-prime of g of x, and times with g-prime of x.

Oh, derivatives can describe motion and show how two things relate;
With them you can optimize and even calculate
Things like the earth’s path around the sun,
Or how to build a ‘coaster that is both safe and fun!

Your last basic’s the quotient rule,
And this one’s quite a mouthful too:
If you start with u over v,
Take u v-prime from u-prime v,
But you’re still not done, you see:
Divide all that by the square of v.

So what’s it all mean? Where do they come from?
Who came up with this stuff, and why is it done?
I could throw you some vocab, like tangent and limit
And Leibniz or Newton, well who knows who did it.
But really for all that, a song’s not up to the task;
If you’re curious my advice is: go take the class!