A "Typical" Calculus Problem

If you’ve taken calculus before you probably have vague recollections of terms like “the chain rule” or “the product rule” or “the quotient rule”… these are all techniques for calculating the derivative of a function when you know the function’s algebraic form. Calculating the derivative of a function is also known as differentiation. And in a typical calculus class you would spend a LOT of time learning how to differentiate various functions…

Below you will see a differentiation problem that is similar to what you might find in a typical calculus class. Read through this problem and think about what it’s asking. Afterwards I’m going to explain why we are not going to spend time solving these kinds of problems in this course.

Differentiation Example Problem

1. A self driving car's position is described as a function of time from t=0 to t=10 by the following equation:

   x(t) = -t^2 + 10t + 5

What is the derivative, \dot{x}(t) of this function?
A graph of x(t) is included below.