# The derivative of the function 2 x + y = 3 by implicit differentiation.

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

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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