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in my calc class, someone noticed that when you take the derivative of the formula for volume of a circle, it becomes the formula for the surface area. anyone know why? and what other shapes is this also true for?
Any surface that, when applying a coating of paint with uniform thickness, is (sufficiently close to) the same kind of surface.
Originally posted by Gale17
umm... i have no clue what that means...
and since we're on the subject of my having no clue... what is this 'nesting of spherical shells'
Originally posted by Gale17
whats is stokes theorem?
A derivative is a mathematical concept that measures the rate of change of a function with respect to one of its variables. In simpler terms, it is the slope of a curve at a specific point.
An explicit derivative is when a function is explicitly written in terms of its independent variable, making it easy to differentiate. An implicit derivative is when a function is not explicitly written in terms of its independent variable, and therefore requires the use of the chain rule to differentiate.
The surface area of a circle is given by the formula A = πr². To find the derivative, we use the power rule and the fact that π is a constant. The derivative of A with respect to r is then 2πr.
The derivative of a function at a specific point is equal to the slope of the tangent line at that point. This means that the derivative gives us the instantaneous rate of change of the function at that point.
Yes, derivatives have a wide range of applications in various fields such as physics, engineering, economics, and more. They can be used to model and analyze rates of change in real-life scenarios, such as predicting the growth of a population or the speed of a moving object.