   Chapter 14.3, Problem 82E

Chapter
Section
Textbook Problem

The temperature at a point (x, y) on a flat metal plate is given by T(x, y) = 60/(1 + x2 + y2), where T is measured in °C and x, y in meters. Find the rate of change of temperature with respect to distance at the point (2, 1) in (a) the x-direction and (b) the y-direction.

(a)

To determine

To find: The rate of change of temperature with respect to distance at the point (2,1) in x-direction if the temperature is given by T(x,y)=60(1+x2+y2) , where T is temperature and x,y in meters.

Explanation

The given function is, T(x,y)=60(1+x2+y2) .

Take the partial derivative of the given function with respect to x and obtain Tx .

Tx=x(60(1+x2+y2))=60(1)(1+x2+y2)2(0+2x+0)=120x(1+x2+y2)2=120x(1+x2+y2)

(b)

To determine

To find: The rate of change of temperature with respect to distance at the point (2,1) in y - direction if the temperature is given by T(x,y)=60(1+x2+y2) , where T is temperature and x,y in meters.

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