   Chapter 3.9, Problem 10E

Chapter
Section
Textbook Problem

Suppose 4x2 + 9y2 = 36, where x and y are functions of t.(a) If d y / d t = 1 3 , find dx/dt when x = 2 and y = 2 3 5 (b) If dx/dt = 3, find dy/dt when x = –2 and y = 2 3 5

To determine

To find: dxdt  when x=2 and y=235 with dydt=13

Explanation

Given:

The given values are dydt=13 and x=2 and y=235.

Formula used:

Chain rule:dydx=dydududx

Calculation:

Since 4x2+9y2=36  where x  and y are the function of the variable t.

Therefore, x and y changes when the variable t changes.

Since dydt=13.

Obtain dxdt when x=2 and y=235.

Differentiate the function 4x2+9y2=36 with respect to the variable t both sides.

ddt(4x2+9y2=36)=ddt(26)4ddt(x2)+9ddt(y2)=04(2x)dxdt+9(2y)dydt=0(8x)d

(b)

To determine

To find: dydt when x=2 and y=235 with dxdt=3.

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