BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 3.5, Problem 4E
To determine

To calculate: The derivative of the function 2x+y=3 by implicit differentiation.

Expert Solution

Answer to Problem 4E

The derivative of the function is 2yx .

Explanation of Solution

Given information:

The function 2x+y=3 .

Formula used:

Thechain rule for differentiation is if f is a function of gthen ddx(f(g(x)))=f'(g(x))g'(x) .

Power rule for differentiation is ddxxn=nxn1 .

Calculation:

Consider the function 2x+y=3 .

Differentiate both sides with respect to x ,

  ddx(2x+y)=ddx(3)ddx(2x)+ddx(y)=0ddx(2x12)+ddx(y12)=0

Recall that power rule for differentiation is ddxxn=nxn1 and chain rule for differentiation is if f is a function of gthen ddx(f(g(x)))=f'(g(x))g'(x) .

Apply it. Also observe that y is a function of x,

  22x+12ydydx=012ydydx=1x

Divide both sides by 2y and simplify,

  12ydydx=1xdydx=2yxdydx=2yx

Thus, the derivative of the function is 2yx .

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