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.)
Multi variable partial differentiation is a mathematical concept used to calculate the rate of change of a function with respect to multiple independent variables. It is an extension of ordinary differentiation, which only involves one independent variable.
The purpose of multi variable partial differentiation is to help us understand how a function changes when multiple independent variables are varied simultaneously. It is especially useful in fields such as physics and economics, where multiple variables are often involved in a single equation.
Solving problems involving multi variable partial differentiation can be challenging because it requires a solid understanding of basic calculus principles and the ability to manipulate multiple variables and equations simultaneously. It may also involve complex mathematical concepts, such as partial derivatives and chain rule.
The best way to improve your skills in solving problems involving multi variable partial differentiation is through practice. Start by mastering the fundamentals of calculus and then gradually work your way up to more complex problems. You can also seek help from a tutor or join a study group to get additional support.
Yes, multi variable partial differentiation has many real-life applications. It is commonly used in fields such as physics, engineering, economics, and statistics to model and analyze complex systems. For example, it can be used to optimize production processes, analyze market trends, and determine the trajectory of a projectile.