The discussion centers on the application of the chain rule in multi-variable calculus, specifically for the function z = f(x - y). Participants clarify that the derivatives dz/dx and dz/dy can be expressed as dz/dx = fu and dz/dy = -fu, leading to the conclusion that dz/dx + dz/dy = 0. This demonstrates the relationship between the variables x and y in the context of partial differentiation. The correct application of the chain rule is essential for solving such problems accurately.
PREREQUISITESStudents and educators in mathematics, particularly those studying calculus and partial differentiation, as well as professionals applying these concepts in fields such as engineering and physics.
LovePhysics said:Homework Statement
If z = f(x-y), show that dz/dx + dz/dy = 0
2. The attempt at a solution
I thought:
dz/dx = fx
dz/dy = -fy
which doesn't make sense really... because its not equal to 0.
or maybe it should be:
dz/dx = dz/df * df/dx = fx * ??
dz/dy = dz/df * df/dy = -fy * ??
Thats great thx.HallsofIvy said:Use the chain rule. If z= f(u) and u= x- y then [itex]\partial f/\partial x= df/du \partial u/\partial x[/itex] and [itex]\partial f/\partial y= df/du \partial u/\partial y[/itex].
(If z= f, then "dz/df" is just 1.)