This exercise proves the Chain Rule without the special assumption made in the text. For any number
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This exercise proves the Chain Rule without the special assumption made in the text. For any number b, define a new function
(a) Show that if we define F(b) = ƒ'(b), then F is continuous at u = b.
(b) Take b = g(a). Show that if x ≠ a, then for all u,
Note that both sides are zero if u = g(a).
(c) Substitute u = g(x) in Eq. (1) to obtain
Eq.(1)
Derive the Chain Rule by computing the limit of both sides as x → a.
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