What is the derivative? Mathematically/or real world? What is the power rule and

Question

1. What is the derivative? Mathematically/or real world?
2. What is the power rule and how do we use it to find a derivative?
3. What is the product rule and how do we use it to find a derivative?
4. What is the quotient rule and how do we use it to find a derivative?
5. What is the chain rule and how do we use it to find a derivative?
6. What information can be obtained from derivatives? Please provide an example from the real world and explain the information that you could gain from it.
7. How do we find higher-order derivatives?
8. How are the higher-order derivatives for f(x) = 3x6 different from the higher-order derivatives of f(x) = 2x-4?

Explanation / Answer

1)

A function which gives the slope of a curve; that is, the slope of the line tangent to a function. The derivative of a function f at a point x is commonly written f '(x). For example, if f(x) =x3 then f '(x) = 3x2. The slope of the tangent line when x = 5 is f '(x) = 3

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