   Chapter 11.4, Problem 2CP ### 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

# (a) Differentiate x 2 +   64 =   y 2 implicitly with respect to time.(b) Suppose we know that y is increasing at 2 units per minute. Use part (a) to find the rate of change of x at the instant when x = 6 and y = 10.

(a)

To determine

To calculate: The value of differentiation of x2+64=y2 implicitly with respect to time.

Explanation

Given information:

The provided function is,

x2+64=y2

Formula used:

Implicit differentiation,

If y is the function of x, then dydt can be calculated by differentiating both side with respect to t and followed by algebraically solving for dydt.

Calculation:

Consider the function,

x2+64=y2

Use the implicit differentiation to find the derivative as,

First differentiate both sides with respect to t as,

ddt(x2)+ddt

(b)

To determine

To calculate: The rate of change of x at the instant when x=6 and y=10 where y is increasing 2 units per minute.

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