If f (x) = x* and g(x) = x³, then f'(x) = 4x³ and g'(x) = 3x². The Chain Rule %3| multiplies derivatives to get 12x5. But f (g(x)) = (x³)ª = x12 and its derivative %3D is NOT 12x5. Where is the flaw?

If f (x) = x* and g(x) = x³, then f'(x) = 4x³ and g'(x) = 3x². The Chain Rule %3| multiplies derivatives to get 12x5. But f (g(x)) = (x³)ª = x12 and its derivative %3D is NOT 12x5. Where is the flaw?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.CR: Chapter 3 Review

Problem 59CR

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Question

If ?(?)=?⁴ and ?(?)=?³, then ?′(?)=4?³ and ?′(?)=3?². The Chain Rule multiplies derivatives to get 12?⁵. But ?(?(?))=(?³)⁴=?¹² and its derivative is NOT 12?⁵. Where is the flaw?

If f(x) = x* and g(x) = x³, then f'(x) = 4x³ and g'(x) = 3x². The Chain Rule
%3D
%3D
multiplies derivatives to get 12x5. But f(g(x)) = (x³)4 = x12 and its derivative
is NOT 12x5. Where is the flaw?

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If f(x) = x* and g(x) = x³, then f'(x) = 4x³ and g'(x) = 3x². The Chain Rule multiplies derivatives to get 12x5. But f(g(x)) = (x³)4 = x¹2 and its derivative is NOT 12x5. Where is the flaw? 1| Page