Proof of second order derivative

In summary, a second order derivative is a mathematical function that represents the rate of change of a derivative. It can be calculated by taking the derivative of the first derivative of a function. It is significant in analyzing functions and understanding graph behavior, providing information about concavity and inflection points. It differs from a first order derivative in that it shows how the rate of change is changing. In real-world applications, it is used in fields such as physics, engineering, and economics to analyze motion, find optimal solutions, and understand market and economic behavior.
  • #1
manish15689
2
0
How to prove that

y''=d2y/dx2

if y=f(x)
 
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  • #2
?
That's just expressing the equivalence between two different types of notation conventions..
 
  • #3
i want to know how does the notation d2y/dx2 come into existence...
 
  • #4
manish15689 said:
i want to know how does the notation d2y/dx2 come into existence...

Leibniz introduced it. Why would that be of any interest??
 

1. What is a second order derivative?

A second order derivative is a type of mathematical function that represents the rate of change of a derivative. It is the rate of change of the rate of change of a given function.

2. How is a second order derivative calculated?

A second order derivative can be calculated by taking the derivative of the first derivative of a function. This is also known as taking the derivative of a derivative or finding the derivative of the derivative.

3. What is the significance of a second order derivative?

A second order derivative is important in analyzing functions and understanding the behavior of graphs. It can provide information about the concavity and inflection points of a function.

4. What is the difference between a first and second order derivative?

A first order derivative represents the instantaneous rate of change of a function, while a second order derivative represents the rate of change of the first derivative. In other words, a second order derivative shows how the rate of change is changing.

5. How is a second order derivative used in real-world applications?

A second order derivative has various applications in fields such as physics, engineering, and economics. It can be used to analyze the motion of objects, determine optimal solutions in optimization problems, and understand the behavior of markets and economies.

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