   Chapter 3.5, Problem 3E

Chapter
Section
Textbook Problem

(a) Find y′ by implicit differentiation.(b) Solve the equation explicitly for y and differentiate to get y′ in terms of x.(c) Check that your solutions to parts (a) and (b) are consistent by substituting the expression for y into your solution for part (a).3. x + y = 1

(a)

To determine

To find: The derivative dydx by implicit differentiation.

Explanation

Given:

The equation x+y=1

Derivative rules:

(1) Chain rule: if y=f(u) and u=g(x)  are both differentiable function, then

dydx=dydududx

(2) Power rule: ddx(xn)=nxn1

(3) Difference rule: ddx(fg)=ddx(f)ddx(g)

(4) Sum rule: ddx(f+g)=ddx(f)+ddx(g)

(5) Constant multiple rule: ddx(cf)=cddx(f)

Calculation:

Obtain the derivative of the given equation.

x+y=1

Differentiate with respect to x on both sides,

ddx(x+y)=ddx(1)

Apply the derivative rules (4),(1) and (2),

ddx(x)+ddx(

(b)

To determine

To find: The equation explicitly for y and dydx.

(c)

To determine

To check: Whether the solutions from part (a) and part (b) are consistent or not.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

In Exercises 1-6, simplify the expression. 3+2x7x

Calculus: An Applied Approach (MindTap Course List)

In Exercises 516, evaluate the given quantity. log22

Finite Mathematics and Applied Calculus (MindTap Course List)

A sample with a mean of M = 8 has X = 56. How many scores are in the sample?

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Evaluate the integrals in Problems 1-32. Identify the formula used.

Mathematical Applications for the Management, Life, and Social Sciences

For f(x, y) = ln(x + y), f(e2, e3) = 2 ln (1 + e) 2 + ln(1 + e) 5

Study Guide for Stewart's Multivariable Calculus, 8th

In Exercise 1320, plot the point on a set of coordinate axes. (1,3)

Finite Mathematics for the Managerial, Life, and Social Sciences 