3.6 The Chain Rule.pdf - 3.6 The Chain Rule The Chain Rule...

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3.6 The Chain Rule Page 1 of 1 The Chain Rule (? ∘ ?) = [? ∘ ?] ⋅ ? that is, (?(?(?))) = ? (?(?)) ⋅ ? (?) With ? = ?(𝑢) and 𝑢 = ?(?) , the Chain rule becomes: ?? ?? = ?? ?𝑢 ?𝑢 ?? If 𝑢 = ?(?) is differentiable, then 1. Generalized Power Rule: ? ?? (𝑢 𝑛 ) = 𝑛 𝑢 𝑛−1 ?𝑢 ?? 2. ? ?? (? 𝑢 ) = ? 𝑢 ?𝑢 ?? Examples: Find the derivative ??/?? . (a) ? = (? 5 + 2? 3 ) 4 (d) ? = ? 4 ? 2? (b) ? = √5? 4 − 2? (e) ? =

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