The temperature at a point (x, y) on a flat metal plate is given by t(x, y) = 45/(6 + 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 (3, 1) in the x-direction and the y-direction. (a) the x-direction °c/m (b) the y-direction °c/m

Change in x direction is

Change in y direction is

Explanation:

The temperature is given by we need to find gradient of temperature to obtain the rate of change thus

Now the rate of change at (3,1) in

1) X direction is given by

2) Y direction is given by

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