. Let: f(x) = 1 /x  (a) Use the limit definition of derivative to find f'(x). (b) Verify your answer to (a) using the Power Rule. (c) Use the Power Rule to find f"(x), f'''(x) and f^(4) (x). Find a pattern in the derivatives and make a conjecture for a formula for f^(n) (x), the nth derivative of f(x)

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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5. Let:

f(x) = 1 /x 

(a) Use the limit definition of derivative to find f'(x).

(b) Verify your answer to (a) using the Power Rule.

(c) Use the Power Rule to find f"(x), f'''(x) and f^(4) (x). Find a pattern in the derivatives and make a conjecture for a formula for f^(n) (x), the nth derivative of f(x).

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