   Chapter 11.3, Problem 49E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problem 11, the derivative y' was found to be y ' = − x y when x 2 + y 2 =   4. (a) Take the implicit derivative of the equation for y' to show that y " = − y + x y ' y 2 (b) Substitute — x/y for y' in the expression for y" in part (a) and simplify to show that y " = ( x 2 + y 2 ) y 3 (c) Does y " =   —   4 / y 3 ? Why or why not?

(a)

To determine

To prove: The equation y=y+xyy2 if y=xy.

Explanation

Given Information:

The provided first derivative is, y=xy.

Formula used:

The quotient rule of derivatives,

ddx[u(x)v(x)]=[v(x)]du(x)dx[u(x)]dv(x)dx[v(x)]2

Proof:

Consider the first derivative,

y=xy

N

(b)

To determine

To prove: The equation y=(x2+y2)y3 if y=xy.

(c)

To determine

The validity of statements y=4y3 if x2+y2=4.

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