   Chapter 3.5, Problem 4E ### 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).4. 2 x − 1 v = 4

(a)

To determine

To find: The derivative dydx by implicit differentiation.

Explanation

Given:

The equation 2x1y=4.

Derivative rules:

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

dydx=dydududx.

(2) Quotient Rule: If f1(x) and f2(x) are both differentiable, then

ddx[f1(x)f2(x)]=f2(x)ddx[f1(x)]f1(x)ddx[f2(x)][f2x]2.

Calculation:

Obtain the derivative of the given equation.

2x1y=4

Differentiate with respect to x on both sides,

ddx(2x1y)=ddx(4)ddx(2x1y1)=ddx(4)ddx(2x1)ddx(y1

(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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