What happens if you can write a function as a composite in differentways? Do you get the same derivative each time? The Chain Rulesays you should. Try it with the functions in Exercises 39 and 40. 39. Find dy/dx if y = cos (6x + 2) by writing y as a compositewith(a) y = cos uandu = 6x + 2.u = 3x + 1.40. Find dy/dx if y = sin (x² + 1) by writing y as a composite(b) y = cos 2uandwith(a) y = sin (u + 1)and u =x2.(b) y = sin uandu = x2 + 1.

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Description: What happens if you can write a function as a composite in differentways? Do you get the same derivative each time? The Chain Rulesays you should. Try it with the functions in Exercises 39 and 40. 39. Find dy/dx if y = cos (6x + 2) by writing y as a

39. Part a). It is given that, y=cos u and u=6x+2 Therefore, dydu=-sin u and dudx=6 So,…

Answered: 39. Find dy/dx if y = cos (6x + 2) by…

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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What happens if you can write a function as a composite in different
ways? Do you get the same derivative each time? The Chain Rule
says you should. Try it with the functions in Exercises 39 and 40.

39. Find dy/dx if y = cos (6x + 2) by writing y as a composite
with
(a) y = cos u
and
u = 6x + 2.
u = 3x + 1.
40. Find dy/dx if y = sin (x² + 1) by writing y as a composite
(b) y = cos 2u
and
with
(a) y = sin (u + 1)
and u =x2.
(b) y = sin u
and
u = x2 + 1.

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