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The derivative of a difference of functions: [f(x)-g(x)] = f(x)-8(x) On short, (f-g)' = f'-g

The derivative of a difference of functions: [f(x)-g(x)] = f(x)-8(x) On short, (f-g)' = f'-g

Calculus: Early Transcendentals
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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Question

Part D

2. Write the proofs for the following derivative rules. a. b. C. d. The derivative of a power function: Note: the power rule works for any real n. The derivative of the natural exponential function: The derivative of a sum of functions: d dx -(x")=; [f(x) + g(x)] = f(x)+g(x)]= )=x²-1 (e) = e On short, (x)' = nxx" On short, (e*)' = e²| d f(x)+g(x) On short, (f+g)' = f'+g' The derivative of a difference of functions: f(x)-g(x)]=f(x)-8(x) On short, (f-g)' = f'-g
Transcribed Image Text:2. Write the proofs for the following derivative rules. a. b. C. d. The derivative of a power function: Note: the power rule works for any real n. The derivative of the natural exponential function: The derivative of a sum of functions: d dx -(x")=; [f(x) + g(x)] = f(x)+g(x)]= )=x²-1 (e) = e On short, (x)' = nxx" On short, (e*)' = e²| d f(x)+g(x) On short, (f+g)' = f'+g' The derivative of a difference of functions: f(x)-g(x)]=f(x)-8(x) On short, (f-g)' = f'-g
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