Partial Differentiation

Question 1

What is a homogeneous function?

Answer 1

A homogeneous function is a function that can be described as
f(kx, ky) = kⁿf(x, y)

This means that, after multiplying each independent variable by the constant ‘k’, f(kx, KY), one can then factor out the constant from the function, and get the original function back, kⁿ f(x, y), where ‘n’ is the degree of the homogeneous function.

Question 2

What is the dy/dx of a function, f(x,Y), where f(x,Y) is a function of independent variables and is (or can be) equated to zero?

Answer 2

dy/dx = -(∂f/∂x) ÷ (∂f/∂y)