   Chapter 3.5, Problem 3E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
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.

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