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

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The discussion centers on solving for the x force component in a physics problem involving the interaction between oxygen atoms in molecules. The user has successfully tackled the partial derivative but is confused about deriving the x component from their current result. A key point raised is the dual meaning of "derive" in mathematics, which could lead to misunderstanding the required steps. Clarification is provided that the user may have applied the wrong interpretation of "derive." The conversation emphasizes the importance of correctly understanding mathematical terminology to proceed with the problem-solving process.
Jorzef
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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
1589488081001.png


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:
1589488302634.png

What do can i do from here on, thank you!
 
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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.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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