3. Definition of the Derivative. Use the definition of the derivative to find the derivatives of the following functions. (f(x+h) – f(x) f'(x) = lim h→0 (ळ)-ै a. g(x) = 3(x – 4)2 b. T(x) = tan(x) (You will need the fact that tan(a + b) = tan(a)+tan(b) and 1-tan(a) tan(b) (sec(x))? = 1+ (tan(x))². c. f(x) = Vx+ 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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3. Definition of the Derivative. Use the definition of the derivative to find the derivatives of
the following functions.
(f(x + h) – f(x)
f'(x) = lim
h→0
h
a. g(x) = 3(x – 4)²
tan(a)+tan(b)
b. T(x) = tan(x) (You will need the fact that tan(a + b)
and
1-tan(a) tan(b)
(sec(x))2 = 1+ (tan(x))².
c. f(x) = Vx+ 2
Transcribed Image Text:3. Definition of the Derivative. Use the definition of the derivative to find the derivatives of the following functions. (f(x + h) – f(x) f'(x) = lim h→0 h a. g(x) = 3(x – 4)² tan(a)+tan(b) b. T(x) = tan(x) (You will need the fact that tan(a + b) and 1-tan(a) tan(b) (sec(x))2 = 1+ (tan(x))². c. f(x) = Vx+ 2
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