7. (Chain Rule): Let ƒ : [a, b] → R, g : [c, d] → R, ƒ([a, b]) ≤ [c, d], and xo = [a, b]. If f is differentiable at xo and g is differentiable at f(xo), then the composition function gof is differentiable at c and (gof)'(c) = g'(ƒ(c)) · f'(c).

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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7. (Chain Rule): Let f: [a, b] → R, g: [c, d] → R, f([a, b]) ≤ [c, d], and xo [a, b]. If f
is differentiable at to and g is differentiable at f(xo), then the composition function
g of is differentiable at c and (go ƒ)'(c) = g'(ƒ(c)) · ƒ'(c).
Transcribed Image Text:7. (Chain Rule): Let f: [a, b] → R, g: [c, d] → R, f([a, b]) ≤ [c, d], and xo [a, b]. If f is differentiable at to and g is differentiable at f(xo), then the composition function g of is differentiable at c and (go ƒ)'(c) = g'(ƒ(c)) · ƒ'(c).
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