Switch the divergence coordinate system

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The discussion focuses on converting the divergence from Cartesian coordinates (x, y, z) to cylindrical coordinates (r, φ, z). The original divergence expression is given as the sum of partial derivatives of the vector components. The user attempted to apply the chain rule but encountered difficulties, prompting requests for clarification on their approach. Participants emphasize the need to see the user's work to identify any errors in the conversion process. The conversation highlights the importance of correctly applying transformation techniques in vector calculus.
oronanschel
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Homework Statement


i have the divergence in the (x,y,z) Cartesian as \frac{dA_x}{dx}+\frac{dA_y}{dy}+\frac{dA_z}{dz}

and the assignment is to transfer it to cylindrical system (r,{\phi},z), by any way i choose.



Homework Equations




tried with the chain rule, but i am doing something wrong, though
i get the gradient in the cylindrical system
 
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It is impossible to tell you what, if anything, you are doing wrong if we cannot see what you did!
 
look at 1 then 2

then there is 1+2

in the left side there are some derivatives , and variables
transformation to explain


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Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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