Open study

is now brainly

With Brainly you can:

  • Get homework help from millions of students and moderators
  • Learn how to solve problems with step-by-step explanations
  • Share your knowledge and earn points by helping other students
  • Learn anywhere, anytime with the Brainly app!

A community for students.

session 42 problem:non-independent variables 3.Now suppose w is as above and x^2y +y^2x = 1. Assuming x is the independent variable, find ∂w/∂x. The answer is here: I don't understand why we should set z = 0.

OCW Scholar - Multivariable Calculus
See more answers at
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Join Brainly to access

this expert answer


To see the expert answer you'll need to create a free account at Brainly

Good question zane120000. We have a three variable equation, x, y, and z. We are told that x and y are related by a constraint equation. That means that any change in x produces a known change in y. The variable y is therefore totally dependent on x. This reasoning is reversible and x could be totally dependent on changes in y, but we are told in the question to assume that it is y that is dependent. But that leaves a third variable hanging there, z. What do we do with that z? Well, we just want to know what the rate of change is for w when x changes. If we allow z to have a value that changes, this corrupts our calculation. We only want to know how w changes when x changes. Therefore we zero out any independent variables other than x.
Thank you for your response,Waynex! I got a deeper understanding with your help! Then I still have a question:When z have a different value from 0,will ∂w/∂x differ?Or will ∂w/∂x varies when a point moves vertically in cartesian coefficient?
That's a great point. And I don't know what the answer is supposed to be, but I did take a look at that while I was going through that pdf. If we did set z to a value other than 0, the x and y variables would show up in more places and the value does seem like it would change. Would that change be linear? If so, then the change is not as interesting as if might be if it was not linear. I suspect that this is like calculating a single variable derivative at a specific point. For instance, if we calculate the derivative of 2x^3=y, we get 6x^2=dy. Perhaps we want to know the rate of change in y at the specific x location of 1, then we get 6(1^2)=dy. Similarly, we could ask what the partial of w with respect to partial x is when z is fixed to 5, and plug in 5 for z.

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

Recently I thought over the question for long.Finally I agree with your opinion :we should ask the partial derivatives in particular point.thank you for you answer again!

Not the answer you are looking for?

Search for more explanations.

Ask your own question