   Chapter 3.9, Problem 12E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# A particle is moving along a hyperbola xy = 8. As it reaches the point (4, 2), they-coordinate is decreasing at a rate of 3 cm/s. How fast is the x-coordinate of the point c hanging at that instant?

To determine

To find: How fast is the x-coordinate of the point changing at that instant. When a particle moving along a hyperbola xy=8 when particle reaches to the point (4,2).

Explanation

Given:

A particle is moving along the hyperbola xy=8. As the particle reaches to the point (4,2),

y-coordinate decreases at a rate of 3cm/s, that is dydt=3cm/s.

Formula used:

(1) Chain rule dydx=dydududx

(2) Product rule of differentiation: ddx(fg)=fddx(g)+gddx(f)

Calculation:

The equation of hyperbola xy=8, where the variables x and y function of the variable t.

Since t changes therefore, the variables x and y also changes.

Since the particle reaches to the point (4,2), y- coordinate decreases at a rate of dydt=3cm/s.

Obtain the derivative dxdt when particle at the point (4,2) on the hyperbola xy=8.

Differentiate xy=8 with respect to t both sides

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