I will derive!

At first I was afraid, what could the answer be?
It said given this position find velocity.
So I tried to work it out but I knew that I was wrong.
I struggled; I cried, “The problem shouldn’t take this long!”
I tried to think, control my nerve …
It’s evident that speed’s tangential to that time–position curve.
This problem would be mine
If I just knew that tangent line
But what to do? Show me a sign!

So I thought back: do calculus,
Way back to Newton and to Leibniz
And to problems just like this.
And just like that when I had given up all hope
I said nope.
There’s just one way to find that slope –
And so now I, I will derive!
Find the derivative of x’s position with respect to time.
It’s as easy as can be –
Just have to take dx/dt –
I will derive, I will derive, hey hey!

And then I went ahead to the second part
But as I looked at it I wasn’t quite sure how to start:
It was asking for the time at which velocity was at a maximum.
And I was thinking, “Woe is me!”
But then I thought, “This much I know:
I gotta find acceleration, set it equal to zero.
Now if only knew what the function was for it …
I guess I’m gonna have to solve for it some way.”

So I thought back: do calculus,
Way back to Newton and to Leibniz
And to problems just like this.
And just like that when I had given up all hope
I said nope.
There’s just one way to find that slope –
And so now I, I will derive!
Find the derivative of velocity with respect to time.
It’s as easy as can be –
Just have to take dv/dt –
I will derive, I will derive …

So I thought back: do calculus,
Way back to Newton and to Leibniz
And to problems just like this.
And just like that when I had given up all hope
I said nope.
There’s just one way to find that slope –
And so now I, I will derive!
Find the derivative of x’s position with respect to time.
It’s as easy as can be –
Just have to take dx/dt –
I will derive, I will derive, I will derive!