Vector and partial derivatives

In summary, the conversation discusses finding the partial derivatives of a scalar function in terms of the position of two charges, with a sub-question involving the use of vectors. The solution involves solving for the magnitude of the distance between the two charges and then taking the partial derivative of the scalar function. There is some confusion about whether the function is a vector or a magnitude, but it is ultimately clarified that it is a scalar function.
  • #1
Crazy Gnome
13
0

Homework Statement



Two charges one located at P at the position (x,y,z) and P' at the position (x',y',z')

Let f= 1/R.
Calculate Fx= partial derivative of f with respect to x.
Calculate Fx'= partial derivative of f with respect to x'.

There are sub question involving the same thing with other variables but if you could help me figure out the first part that should go easy.

The Attempt at a Solution



I solved R to be = (x-x')i + (y-y')j + (z-z')k... i think that's right but I do not know how to go about finding the partial derivatives of f. I have never really worked with vectors let alone inverse vectors with calculus.
 
Physics news on Phys.org
  • #2
There is no such thing as an 'inverse vector'. I would guess they mean R=|(x,y,z)-(x',y',z')|, Which is R=sqrt((x-x')^2+(y-y')^2+(z-z')^2).
 
  • #3
Dick said:
There is no such thing as an 'inverse vector'. I would guess they mean R=|(x,y,z)-(x',y',z')|, Which is R=sqrt((x-x')^2+(y-y')^2+(z-z')^2).

Right, I got that part. But what is a partial derivative of 1/ a vector?
 
  • #4
It can't be a vector. 1/'a vector' doesn't make any sense. Are you sure they didn't write 1/|R|? It's just the partial derivative of a scalar function.
 
  • #5
Dick said:
It can't be a vector. 1/'a vector' doesn't make any sense. Are you sure they didn't write 1/|R|? It's just the partial derivative of a scalar function.

Right *bangs head against the wall*. The only difference on the homework sheet between the vector and the magnitude is the vector is in bold. My stupid mistake.


-Thanks
 

Related to Vector and partial derivatives

1. What is a vector derivative?

A vector derivative is a mathematical operation that calculates the rate of change of a vector with respect to a given variable. It is represented as dV/dx, where V is the vector and x is the variable. It measures how much the vector changes in magnitude and direction as the variable changes.

2. How is a partial derivative different from a regular derivative?

A partial derivative is a derivative that measures the rate of change of a function with respect to one of its variables, while holding all other variables constant. In contrast, a regular derivative measures the rate of change of a function with respect to a single variable. In other words, a partial derivative is a generalization of a regular derivative.

3. What is the chain rule for vector derivatives?

The chain rule for vector derivatives is a rule that allows us to calculate the derivative of a composite function, where the input of one function is used as the input of another. It states that the derivative of a composite function is equal to the product of the derivatives of each individual function, multiplied together.

4. How are vector and partial derivatives used in physics?

Vector and partial derivatives are used extensively in physics to model and understand complex systems. They are used to calculate the velocity and acceleration of objects in motion, as well as the rate of change of physical quantities such as force, energy, and electric fields. They are also used in thermodynamics, fluid mechanics, and other areas of physics to study how systems change over time.

5. What are some real-life applications of vector and partial derivatives?

Vector and partial derivatives are used in a variety of real-life applications, including engineering, economics, and computer graphics. In engineering, they are used to analyze and design systems such as bridges, airplanes, and electronic circuits. In economics, they are used to model and predict changes in supply and demand. In computer graphics, they are used to create realistic animations and special effects in movies and video games.

Similar threads

Lagrange multipliers understanding
    • Calculus and Beyond Homework Help
Replies
8
Views
558
Multivariable calculus proof involving the partial derivatives of an expression
    • Calculus and Beyond Homework Help
Replies
4
Views
696
Partial Derivative Simplification
    • Calculus and Beyond Homework Help
Replies
3
Views
844
Find f(x,y) given partial derivative and initial condition
    • Calculus and Beyond Homework Help
Replies
6
Views
624
Multivariable calculus problem involving partial derivatives along a surface
    • Calculus and Beyond Homework Help
Replies
9
Views
796
Calculating the partial derivative in polar coordinates
    • Calculus and Beyond Homework Help
Replies
3
Views
2K
How should I use the Jacobi equation to show this?
    • Calculus and Beyond Homework Help
Replies
4
Views
761
How should I use the Jacobi equation to determine the nature of this?
    • Calculus and Beyond Homework Help
Replies
5
Views
691
Calculate this Integral around the Circular Path using Green's Theorem
    • Calculus and Beyond Homework Help
Replies
3
Views
445
For this Partial Derivative -- Why are different results obtained?
    • Calculus and Beyond Homework Help
Replies
23
Views
1K

Hot Threads

Recent Insights

Back
Top