Question

The temperature at a point (x, y) on a flat metal plate is given by t(x, y) = 23/(8 + 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 (1, 1) in the x-direction and the y-direction.

Answer 1

∂t/∂x = -46x/(8 +x² +y²)²
∂t/∂y = -46y/(8 +x² +y²)²

At (x, y) = (1, 1)
.. ∂t/∂x = -46/100
.. ∂t/∂y = -46/100