1. Scott Pauls Department of Mathematics Dartmouth College
Math 3, Fall 2015
Scott Pauls
Department of Mathematics
Dartmouth College
Class /5/2015

2. Seating
11 - the W𝜙ΣS 10 - Don't drink and derive 9 - Apple 𝜋 4 - The Dirty Derivatives 3 - Too cool to function 2 - Gee I'm a tree 1 - Push it to the limit 8 - ∞ and beyond 7 - Gettin' triggy with it 6 - Shapes on a plane 5 - Kool by induction 1 2 3 4 5 6 7 8 9 10 11
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3. Rules, rules, rules…
Sums: 𝑑 𝑑𝑥 𝑓 𝑥 +𝑔 𝑥 = 𝑑 𝑑𝑥 𝑓 𝑥 + 𝑑 𝑑𝑥 𝑔 𝑥 Constants: 𝑑 𝑑𝑥 𝐶=0, 𝑑 𝑑𝑥 𝐶𝑓 𝑥 =𝐶 𝑑 𝑑𝑥 𝑓 𝑥 Power rule: 𝑑 𝑑𝑥 𝑥 𝑛 =𝑛 𝑥 𝑛−1 , 𝑛≠0 𝑑 𝑑𝑥 𝑥 0 =0 Product rule: 𝑑 𝑑𝑥 𝑓 𝑥 𝑔 𝑥 =𝑔 𝑥 𝑑 𝑑𝑥 𝑓 𝑥 +𝑓 𝑥 𝑑 𝑑𝑥 𝑔(𝑥) Quotient rule: 𝑑 𝑑𝑥 𝑓 𝑥 𝑔 𝑥 = 𝑔 𝑥 𝑑 𝑑𝑥 𝑓 𝑥 −𝑓 𝑥 𝑑 𝑑𝑥 𝑔(𝑥) 𝑔 𝑥 2
Class /5/2015

4. Special functions and their derivatives
𝑑 𝑑𝑥 sin 𝑥 = cos 𝑥 𝑑 𝑑𝑥 cos 𝑥 =− sin 𝑥 𝑑 𝑑𝑥 𝑒 𝑥 = 𝑒 𝑥 𝑑 𝑑𝑥 ln 𝑥 = 1 𝑥
Class /5/2015

5. Finding the quotient rule using the product rule
Class /5/2015

6. Triage problems Find 𝑓′(𝑥) where 𝑓 𝑥 = 𝑥 3 sin⁡(𝑥) 𝑓 𝑥 = ln 𝑥 tan 𝑥
𝑓 𝑥 = −4+ sin 𝑥 𝑥+ cos 𝑥
𝑓 𝑥 = 𝑒 𝑥 xcsc 𝑥
Class /5/2015

7. Make your own!
In groups, make two or three problems which can be solved using the following outlines:
Step 1: Quotient rule
Step 2: Power rule
Step 3: Special differentiation formula B.
Step 1: Product rule
Step 2: Special differentiation formula C.
Create your own set of steps and associated problems. Try to make the problems as hard as possible!
Class /5/2015