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L2: The product and quotient rule (Calculus review)
HW: Page 383; Review Set 15A # 3, 8, 9 Page 383; Review Set 15B # 1bc, 3 Page 384; Review Set 15C
# 1, 5, 8
Product rule:
If p(x) = f(x)g(x) then determine p’(x) using “First Principles”
p’(x) =
Therefore, the product rule is described as:
p(x)= f(x)g(x) then p’(x)=
Ex1: What is p’(x) if f(x)=2x and g(x)= x2-5?
Quotient rule:
Therefore, the quotient rule is described as:
𝒇(𝒙)
q(x)=𝒈(𝒙) then q’(x)=
Ex2: What is y’ for 𝑦 =
𝑥 2 +𝑥−2
𝑥 3 +6
?
Chain rule:
Chain rule in prime (Lagrange) Notation:
Chain rule in Leibniz Notation:
Let y=f(u) and u= g(x)
Ex3: To differentiat 𝑓(𝑥) = √3𝑥 2 − 4𝑥 + 1