Proving Chain Rule for Partial Derivatives in Calculus 3 Extra Credit Problem

In summary, the conversation is about a person seeking help with an extra credit problem involving proving the equation dx/dy * dy/dz * dz/dx = -1 using partial derivatives. They are unsure if the chain rule should be used and are looking for assistance. The problem is not stated in full and the solution involves treating the variables as quotients and using the rules of implicit differentiation and partial derivatives.
  • #1
ACLerok
194
0
Hi I'm having trouble with this extra credit problem I've been given. I am supposed to prove:

dx/dy * dy/dz * dz/dx = -1 (partial derivatives)

I think I'm supposed to use the chain rule but not sure. Can anyone help me out?
 
Physics news on Phys.org
  • #2
ACLerok said:
Hi I'm having trouble with this extra credit problem I've been given. I am supposed to prove:

dx/dy * dy/dz * dz/dx = -1 (partial derivatives)

I think I'm supposed to use the chain rule but not sure. Can anyone help me out?
This is not the complete statement of the problem. One has to know what the function is. Please provide the complete problem as given to you.

AM
 
  • #3
sorry nope.. it's all i was given.
 
  • #4
It's true in general. matt grime likes to bring it up now and then!

How did trying the chain rule go? (I assume you tried it, since you thought it would be a good idea) How did you set up the problem?
 
  • #5
i figured if you treat them as quotients you can 'multiply' by dy/dx, dz/dy, and dx/dz to cancel them out but that wouldn't work.. I only said the chain rule cause my TA gave us that hint
 
  • #6
firstly, it must be assumed f(x,y,z)=0 implicitly defines x as a function of y and z and y as a function of x and z and z as a function of x and y.

then just use the usual rules of implicit differentiation and partial derivatives.
 

Related to Proving Chain Rule for Partial Derivatives in Calculus 3 Extra Credit Problem

1. What is "Calculus 3 extra credit"?

"Calculus 3 extra credit" refers to additional assignments or projects that can be completed in a Calculus 3 class to earn extra points towards a student's grade. These are typically offered as optional assignments and are not required for the course.

2. How much extra credit can I earn in Calculus 3?

The amount of extra credit available in Calculus 3 varies depending on the instructor and the specific assignments offered. It is important to carefully read the instructions and guidelines for each extra credit opportunity to determine the potential amount of points that can be earned.

3. Are extra credit assignments in Calculus 3 difficult?

The difficulty level of extra credit assignments in Calculus 3 can vary. Some assignments may be more challenging than others, but they are designed to provide an opportunity for students to push themselves and apply their knowledge in new ways. It is important to carefully consider the time and effort required before taking on an extra credit assignment.

4. Can extra credit make a significant impact on my grade in Calculus 3?

The impact of extra credit on a student's grade in Calculus 3 will depend on the amount of points available and the student's current grade. For some students, completing extra credit may result in a noticeable increase in their grade, while for others it may only have a small impact. It is important to consider the potential benefits before deciding to pursue extra credit.

5. How do I know if I am eligible for extra credit in Calculus 3?

Eligibility for extra credit in Calculus 3 is typically determined by the instructor. Some instructors may offer extra credit to all students, while others may require students to meet certain criteria before they can participate. It is important to consult with the instructor or check the course syllabus to determine if you are eligible for extra credit opportunities.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
795
  • Introductory Physics Homework Help
Replies
4
Views
215
Replies
33
Views
2K
  • Calculus and Beyond Homework Help
Replies
2
Views
971
  • Calculus and Beyond Homework Help
Replies
7
Views
864
  • Science and Math Textbooks
Replies
9
Views
1K
  • Differential Geometry
Replies
2
Views
603
Replies
2
Views
205
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Science and Math Textbooks
Replies
3
Views
831
Back
Top