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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

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).

2. 2x2 + x + xy = 1

(a)

To determine

To find: The derivative dydx by implicit differentiation.

Explanation

Given:

The equation 2x2+x+xy=1.

Derivative rules:

(1) Product Rule: ddx[f1(x)f2(x)]=f1(x)ddx[f2(x)]+f2(x)ddx[f1(x)]

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

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

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

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

Calculation:

Obtain the derivative of 2x2+x+xy=1.

Consider 2x2+x+xy=1

(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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