Relevant equations the derivative equation

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The discussion revolves around finding the rate of change of the surface area of a right circular cylinder with respect to height while keeping the radius constant. The formula for surface area is given as A = 2πr(r + h). The user expresses confusion about differentiating with respect to h since it appears only in one term. They attempt to manipulate the equation but are unsure about their approach, particularly regarding the presence of h in the derivative. Guidance is sought on how to correctly express the area in terms of h and apply the derivative.
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calculus - derivatives
1. Homework Statement

the total surface area of a right circular cylinder is given by the formula: (A = 2Pir(r + h) ).
where r is the radius and h is the height.
sub part a) find the rate of change of A with respect to h is r remains constant

**i know how to take derivatives. the only thing is that in this case, I am not sure how to take the derivative of h since it is only present in one term.

2. Homework Equations
the derivative equation
dA / dr


3. The Attempt at a Solution
i first distributed the 2pir, to yield
2pir^2 + 2pirh
2pir^2(h/h) + 2pirh -- i added the (h/h), which is like multiplying by 1, to add h to the first term- I am not sure if this is correct, but i was just guessing.

h (2pir^2 h^-1 + 2pi r)
now i am stuck here. i can't take the derivative of all the h's in my problem, because one h is still present in the equation.
**below is my attempt to still work with it.
dA/dh = 1 times [-1(2pir^2h^-2) + 2pir
final answer: (-2pir^2h^-2) + 2pir
please can someone guide me on the technique i should use for getting the area to be in terms of h. any and all replies are welcome and appreciated
 
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Hint: What's the derivative of a constant function?
 
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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