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myria36

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myria36

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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