Substituting the simplified numerator back into the derivative formula and simplifying, we have 56х — 56а f'(a) lim (x + 8)(a + 8) х — а 56 lim х — а r - a Xa (x + 8)(a + 8)(x – a) 56 = lim 56 Xa (x + 8)(a + 8) Ftep 4 Evaluating this limit, and replacing a with t and f with G, we conclude that the derivative is as follows. 56 G'(t) = (1+b)²

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Step 3
Substituting the simplified numerator back into the derivative formula and simplifying, we have
56х — 56а
f'(a) = lim
(х + 8)(а + 8)
Xa
X — а
56
lim
х — а
%D
a
(x + 8)(a + 8)(x – a)
56
lim
56
Xa
(х + 8)(а + 8)
Step 4
Evaluating this limit, and replacing a with t and f with G, we conclude that the derivative is as follows.
56
G'(t)
(1+b)?
Submit
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Transcribed Image Text:Step 3 Substituting the simplified numerator back into the derivative formula and simplifying, we have 56х — 56а f'(a) = lim (х + 8)(а + 8) Xa X — а 56 lim х — а %D a (x + 8)(a + 8)(x – a) 56 lim 56 Xa (х + 8)(а + 8) Step 4 Evaluating this limit, and replacing a with t and f with G, we conclude that the derivative is as follows. 56 G'(t) (1+b)? Submit Skip (you cannot come back)
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