Today’s soundtrack is *Extol: The Blueprint Dives*, a metal album with alternating singing and growls, fascinating polyrhythms, and layered song structures.

This evening, I’m reading Martin Gardner’s third (and final) preliminary chapter of Thompson’s *Calculus Made Easy*, titled “What is a Derivative?”

Algebraically speaking, Gardner (1998) says that a derivative is a function that tells us at what rate our dependent variable changes in relation to the independent variable’s rate of change. We can also describe a derivative geometrically: A derivative “determines the exact slope of the tangent to a function’s curve at any specified point along the curve” (Thompson, 1998, p. 34).

An example given is the well-known function *y*=*x*², the graph of which I’ve added on the right. Its derivative is 2*x*, because the dependent variable (*y*) is growing at 2*x* the rate of the independent variable (*x*).

That’s it for today! Next time, we’ll start in on the book proper!

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