If ry3 + y2 + 2r2-2 + 6y (i) determine dy, where r is an independent variable and y is a function of r. Simplify as much as possible. (ii) Find the equation of the tangent line at -1 dr

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...
icon
Related questions
Question
If ry3 + y2 + 2r2-2 + 6y (i) determine dy, where r is an independent variable
and y is a function of r. Simplify as much as possible. (ii) Find the equation of the
tangent line at -1
dr
Transcribed Image Text:If ry3 + y2 + 2r2-2 + 6y (i) determine dy, where r is an independent variable and y is a function of r. Simplify as much as possible. (ii) Find the equation of the tangent line at -1 dr
Expert Solution
Step 1

To calculate the derivative that is dy/dx of the function xy3+y2+2x2=2+6y and also calculate the equation of the tangent line at x=1. Now, first derivate the function then uses the formula for the tangent line to evaluate the equation of the tangent line.

Step 2

Consider the provided equation xy3+y2+2x2=2+6y. Differentiate the provided equation with respect to x.

Calculus homework question answer, Step 2, Image 1
Step 3

Further simplify the above differential equation.

Calculus homework question answer, Step 3, Image 1
Step 4

At the point x=1 the coordinate of y=0. Then, substitute (x,y)=(1,0) in the above calculated derivative of the provided equation.

Calculus homework question answer, Step 4, Image 1
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 8 steps with 5 images

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning