¿Te dan la curva y no sabes cuál es la tangente? ¿Conoces la posición punto a punto, pero no sabes la velocidad?... Deriva !

Letra después del salto

**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, “A 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!

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, “A 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 to 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 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!

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 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 sure quite 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’ve gotta find acceleration, set it equal to zero.

Now if I only knew what the function was for a.

I guess I’m gonna have to solve for it someway.

But as I looked at it I wasn’t sure quite 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’ve gotta find acceleration, set it equal to zero.

Now if I only knew what the function was for a.

I guess I’m gonna have to solve for it someway.

So I thought back to 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.

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 to 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 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!

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 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!