If f(x) = f'(x) = f'(4) = tan x - 5 sec x 3x² tan(x) sec(x) 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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If f(x) =
ƒ'(x) =
ƒ'(4) =
=
tan x
sec x
5
3x² tan(x)
sec(x)
X
Transcribed Image Text:If f(x) = ƒ'(x) = ƒ'(4) = = tan x sec x 5 3x² tan(x) sec(x) X
Expert Solution
Step 1: Define the Quotient Rule:

The Quotient Rule:

open parentheses f over g close parentheses to the power of apostrophe equals fraction numerator f apostrophe times g minus g apostrophe times f over denominator g squared end fraction

Use the common derivatives:

fraction numerator d over denominator d x end fraction open parentheses tan open parentheses x close parentheses close parentheses equals sec squared open parentheses straight x close parentheses
fraction numerator d over denominator d x end fraction open parentheses sec open parentheses straight x close parentheses close parentheses equals sec open parentheses straight x close parentheses tan open parentheses straight x close parentheses

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