Two young mathematicians discuss the chain rule.

Check out this dialogue between two calculus students (based on a true story):
Devyn
Riley! Something is bothering me.
Riley
What is it?
Devyn
I have broken calculus.
Riley
How?
Devyn
Check this out, we know that:
Riley
Right.
Devyn
But I also know that the derivative is the slope of the tangent line at a point.
Riley
Right!
Devyn
But check out this plot of that’s zoomed in around zero:
Riley
Ok…
Devyn
Well, , but the slope of this line is totally not one! What’s going on here?

This problem that Riley and Devyn are having is somewhat subtle.

What mistake is being made?
Riley did not plot . Riley did not take the derivative correctly. Riley was working in degrees, not radians. Riley computed the slope incorrectly.