Finding Derivatives with a Constant Radius

In summary, the formula for the total surface area of a right circular cylinder is A = 2Pir(r + h), where r is the radius and h is the height. To find the rate of change of A with respect to h, if r remains constant, the derivative of the equation is needed. After distributing 2pir, the equation becomes 2pir^2 + 2pirh. The next step is to factor out h and take the derivative, resulting in dA/dh = (-2pir^2h^-2) + 2pir. However, there is still one h present in the equation, so the final answer cannot be simplified further.
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myria36
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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.

Homework Equations


the derivative equation


The Attempt at a Solution


i first ditributed the 2pir, to yield
2pir^2 + 2pirh
2pir^2(h/h) + 2pirh
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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Don't ever double post again, ok?
 

FAQ: Finding Derivatives with a Constant Radius

What is a derivative in calculus?

A derivative in calculus is a mathematical concept that represents the rate of change of a function. It is the slope of a tangent line at a specific point on a graph.

How is a derivative calculated?

A derivative is calculated using the limit definition of the derivative, which involves finding the slope of a line between two points on a graph as the points get closer and closer together. It can also be calculated using various derivative rules and formulas.

What is the purpose of finding derivatives?

The main purpose of finding derivatives is to analyze the behavior of functions and to solve various problems involving rates of change and optimization. Derivatives are also used in many fields such as physics, engineering, and economics.

What is the relationship between derivatives and tangents?

Derivatives and tangents are closely related as the derivative of a function represents the slope of the tangent line at a specific point on the graph of that function. The tangent line is a line that touches the graph of a function at only one point and is parallel to the graph at that point.

What are some real-life applications of derivatives?

Some real-life applications of derivatives include calculating rates of change in physics and engineering problems, determining the maximum or minimum values of a function in optimization problems, and analyzing the growth and decay of populations in biology and economics.

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