SUNY Geneseo Department of Mathematics
Math 221 02
Fall 2020
Prof. Doug Baldwin
This discussion builds your ability to use some core differentiation rules, as discussed in “The Basic Rules,” “The Power Rule,” and “The Sum, Difference, and Constant Multiple Rules” in section 3.3 of our textbook.
Use differentiation rules to find the following derivatives. Post at least one response (comment, suggestion, partial answer, question, etc.; responses don’t have to be complete answers) to at least one of the questions by class time on Thursday, September 24.
Find formulas for f′(x) if...
\[f(x) = 3x + 2\] \[f(x) = 5x^3 - 6x^2 + 2x + 9\]Here’s a function in a form you don’t immediately know how to differentiate, but can you find a way to use the rules from the reading (and only those rules) to take its derivative?
\[g(t) = 3 (2t-1)(t+5)\]Here are a couple of questions that are previews of things we’ll talk about in more depth on Friday:
If derivatives are functions, does that mean that derivatives can have derivatives? If so, can you find the derivative of the derivative of
\[h(s) = s^4 - 6s^2 + 8\]Can you find a function whose derivative is
\[f(x) = 3x^2 - 2x\]In other words, can you find a function G(x) such that G′(x) = f(x)?