The temperature at a point (x, y) on a flat metal plate is given by t(x, y) = 54/(7 + 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, 3) in the x-direction and the y-direction.

dt/dx = -0.373702

dt/dy =  -1.121107

Explanation:

Given data

T(x, y) = 54/(7 + x² + y²)

to find out

rate of change of temperature with respect to distance

solution

we know function

T(x, y) = 54 /( 7 + x² + y²)

so derivative it x and y direction i.e

dt/dx = -54× 2x / (7 +x² + y²)²    1

dt/dy = -54× 2y / (7 + x² + y²)²      2

now put the value point (1,3) as x = 1 and y = 3 in equation 1 and 2

dt/dx = -54× 2(1) / (7 +(1)² + (3)²)²  

dt/dx = -0.373702

and

dt/dy =  -54× 2(3) / (7 + (1)² + (3)²)²

dt/dy =  -1.121107

so easy. just google the electromagnetic waves and it’ll pop up.