Question

The temperature at a point (x,y) on a flat metal plate is given by T(x,y)=19/(2+x^2+y^2), where T is measured in Celsuis and x,y in meters. Find the rate of change of temperature with respect to distance at the point (1,2) in the following directions.
(a) the x-direction
(b) the y-direction

Answer 1

Just need to take partial derivatives of the function with respect to x and y then plug in the point coordinates

dT/dx = -38x/(2 + x^2 + y^2)^2
dT/dy = -38y/(2 + x^2 + y^2)^2 (only difference is the y in the numerator)

so at point 1,2
dT/dx = -38/49 = -0.7755
dT/dy = -76/49 = -1.551