Computing a change in the hypotenuse of a triangle using differentials?

samlech24: Computing a change in the hypotenuse of a triangle using differentials?
a right triangle has sides x=12 inches and y=5 inches. Let z denote the length of the hypotenuse. If x is decreased by 1/100 of an inch and y is increased by 1/50 of an inch, can you compute the approximate resulting change in z using differentials?

Answers and Views:

Answer by nosf37
Change Z = dz/dx * change x + dz/dy*change y
where
dz/dx = d/dx [ sqrt(x^2+y^2) ] = x / [sqrt(x^2 + y^2)]
dz/dy = d/dy [ sqrt(x^2+y^2) ] = y / [sqrt(x^2 + y^2)]

x = 12, y = 5

dz/dx = 12/13
dz/dy = 5 / 13
change x = -1/100
change y = 1 /50

change Z = 12/13*(-1/100) + 5/13*(1/50)
change Z = -1/650 = -0.00154 (inch)