# How can I solve for the x force component in this force expression?

• Jorzef
In summary, the person is seeking help with a problem involving deriving the expression for the x force component exerted by an oxygen atom. They have already attempted the problem and are stuck on the next step. They also mention confusion with the meaning of "derive" in this context.
Jorzef
Homework Statement
Derive the expression to the x force component exerted by an oxygen atom of a molecule j over the oxygen atom of a i molecule knowing that the force expression is given by (equation on attempt at a solution)
Relevant Equations
Equations on attempt at a solution

Hello everyone, I'm stuck doing this problem, I've tackled the partial derivative but i can't figure out the derive for x component part, i solved the partial derivative part, i came to this result:

What do can i do from here on, thank you!

Jorzef said:
Homework Statement:: Derive the expression to the x force component exerted by an oxygen atom of a molecule j over the oxygen atom of a i molecule knowing that the force expression is given by (equation on attempt at a solution)
Relevant Equations:: Equations on attempt at a solution

View attachment 262781

Hello everyone, I'm stuck doing this problem, I've tackled the partial derivative but i can't figure out the derive for x component part, i solved the partial derivative part, i came to this result:
View attachment 262782
What do can i do from here on, thank you!
"Derive" has two meanings in mathematics. It can mean the differential calculus operation of taking a derivative, or it can simply mean to obtain one equation from others by algebraic means.
I have the feeling you have applied the wrong one.

## 1. What is the derivative of a vector?

The derivative of a vector is a mathematical operation that represents the rate of change or slope of a vector at a particular point. It is essentially the vector equivalent of a derivative for a scalar function.

## 2. How is the derivative of a vector calculated?

The derivative of a vector is calculated by taking the derivative of each component of the vector separately. This can be done using the standard rules of differentiation, such as the product rule and chain rule.

## 3. What is the physical interpretation of the derivative of a vector?

The physical interpretation of the derivative of a vector is the instantaneous velocity or direction of motion of an object at a particular point in time. It can also represent the rate of change of a physical quantity, such as displacement or force, with respect to time.

## 4. Can the derivative of a vector be a vector itself?

Yes, the derivative of a vector can be a vector itself. This is because the derivative operation preserves the direction and magnitude of the original vector, resulting in a new vector with the same direction and magnitude as the original.

## 5. What are the applications of the derivative of a vector in science?

The derivative of a vector has many applications in science, particularly in physics and engineering. It is used to calculate the motion of objects, such as projectiles and planets, and to model physical phenomena, such as fluid flow and electric fields. It is also essential in optimization problems and in understanding the behavior of complex systems.

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