Step 1 Let D be the distance between the origin and a moving point on the graph of y = sin 3x. D = Step 3 Step 2 Substitute y sin 3x in the formula for distance. x² + 1 D = D = Differentiate D = dD dt = = = = x² + = x² sin²3x d (x² +sin² 3x)1/2 + y² x2 + sin23x with respect to t and simplify. √x² + sin² 3x (x² + sin² 3x)-¹/2 (x² + sin² 3x) dt (sin (3x))² (x²+ sin ²3x)-1/²(2 2x + 2 sin 3x x + 3sin 3x cos 3x (x² + sin² 3x)-1/2(x + 3sin 3x cos 3x)- dx dt Submit Skip (you cannot come back) 1/2 dx dt X dx dt
Step 1 Let D be the distance between the origin and a moving point on the graph of y = sin 3x. D = Step 3 Step 2 Substitute y sin 3x in the formula for distance. x² + 1 D = D = Differentiate D = dD dt = = = = x² + = x² sin²3x d (x² +sin² 3x)1/2 + y² x2 + sin23x with respect to t and simplify. √x² + sin² 3x (x² + sin² 3x)-¹/2 (x² + sin² 3x) dt (sin (3x))² (x²+ sin ²3x)-1/²(2 2x + 2 sin 3x x + 3sin 3x cos 3x (x² + sin² 3x)-1/2(x + 3sin 3x cos 3x)- dx dt Submit Skip (you cannot come back) 1/2 dx dt X dx dt
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
![=
Find the rate of change of the distance between the origin and a moving point on the graph y
Step 1
Let D be the distance between the origin and a moving point on the graph of y
=
+ y²
D =
Step 2
Substitute y sin 3x in the formula for distance.
D = √ x² + y²
Step 3
D =
dD
dt
Differentiate D = x² + sin²3x with respect to t and simplify.
=
x² + sin²3x
=
=
d
(√x² + sin² 3x
dt
d
-(x² + sin² 3x)¹/2
(x²
dt
—— (x² + sin² 3x)-¹/²/(x² + sin² 3x)
=
dt
(sin (3x))²
1
(x² + sin² 3x)-1/²(2x
-1/2 2x + 2 sin 3x
dx
(x² + sin² 3x)−1/2(x + 3sin 3x cos 3x)-
dt
x + 3sin 3x cos 3x
Submit Skip (you cannot come back)
dx
1/2
) -2
dt
X
dx
sin 3x.
sin(3x) if dx/dt = 7 centimeters per second.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab6702de-5579-4c14-bacb-4d8e7e421acd%2F55b0c7e4-4c4d-40cc-b3e0-51f7c3145847%2Fd6ojsat_processed.png&w=3840&q=75)
Transcribed Image Text:=
Find the rate of change of the distance between the origin and a moving point on the graph y
Step 1
Let D be the distance between the origin and a moving point on the graph of y
=
+ y²
D =
Step 2
Substitute y sin 3x in the formula for distance.
D = √ x² + y²
Step 3
D =
dD
dt
Differentiate D = x² + sin²3x with respect to t and simplify.
=
x² + sin²3x
=
=
d
(√x² + sin² 3x
dt
d
-(x² + sin² 3x)¹/2
(x²
dt
—— (x² + sin² 3x)-¹/²/(x² + sin² 3x)
=
dt
(sin (3x))²
1
(x² + sin² 3x)-1/²(2x
-1/2 2x + 2 sin 3x
dx
(x² + sin² 3x)−1/2(x + 3sin 3x cos 3x)-
dt
x + 3sin 3x cos 3x
Submit Skip (you cannot come back)
dx
1/2
) -2
dt
X
dx
sin 3x.
sin(3x) if dx/dt = 7 centimeters per second.
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