18. Applying the sum (difference) rule, what is the derivative of the givenfunction?F(x): =sin x - cos xtan xF'(x) = sin x + cos x + sec² xF'(x) = sin x - cos x + sec² xbF'(x) = sin x + cos x - sec² xa

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Answered: 18. Applying the sum (difference) rule,…

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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(a) From sin2 x + cos2 x = 1, we have f(x) + g(x) = 1. Take the derivative of both sides of this equation to obtain f' (x) + g' (x) = 0. This implies f'(x) = -g'(x). (b) f' (x) = 2 sin x cos x, and g'(x) = 2(cosx)(-sinx) = -2sin x cos x. So, f'(x) = -g'(x).
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18. Applying the sum (difference) rule, what is the derivative of the given function? F(x) = sin x cos x - tan x F'(x) = sin x + cos x + sec² x F'(x) = sin x - cos x + sec² x O c F'(x) = sin x + cos x - sec² x