How Do You Solve the Second Derivative of a Potential Function in Physics?

In summary, the conversation is about solving a physics problem involving finding the potential function through differentiation. The function is given as \Psi = Axe-kx with constants A and k, and the desired derivative is d2 \Psi/dx2. The person initially suggests just differentiating twice, but realizes they need to use the product and chain rules for this particular function. They also mention using a website called Wolfram Alpha for assistance.
  • #1
cpamieta
10
0

Homework Statement


Well this is a physics problem, need find the potential function



Homework Equations


[itex]\Psi[/itex] =Axe-kx A and k are constants
I need to find d2 [itex]\Psi[/itex]/dx2


The Attempt at a Solution


I thought u would just take the derivative two times
but just d[itex]\Psi[/itex]/dx = Ae-kx-kAxe-kx
Would i do something like this?
http://tutorial.math.lamar.edu/Classes/DE/Linear.aspx
thanks
 
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  • #2
What's the problem with just differentiating it again?
 
  • #3
i forgot how you do a differential equation, i have the solutions. I want to know how you do the dΨ/dx
i thought it would just be dΨ/dx= -A/ke-kx Its been a long summer lol
 
  • #4
You don't have a differential equation. You're simply differentiating a function twice.

For this particular function, you need to use the product rule and chain rule, and you need to know how to differentiate a polynomial and an exponential.
 
  • #5
o ok thxs the wolfan alpha thing said it was when i typed it in. It also gave somthing different
 

FAQ: How Do You Solve the Second Derivative of a Potential Function in Physics?

What is a differential equation?

A differential equation is a mathematical equation that relates the rate of change of a variable to the value of the variable itself. It involves derivatives, which represent the instantaneous rate of change of a function.

Why do we need to solve differential equations?

Differential equations are used to model real-world phenomena in fields such as physics, engineering, economics, and biology. By solving these equations, we can make predictions and understand the behavior of these systems.

What are the different methods for solving differential equations?

There are several methods for solving differential equations, including separation of variables, substitution, and using integrating factors. The specific method used depends on the type and complexity of the equation.

How do I know which method to use to solve a differential equation?

The best method to use for solving a differential equation depends on the type of equation, the initial conditions, and any other given information. It is important to carefully analyze the equation and choose the most appropriate method.

What is the importance of boundary conditions in solving differential equations?

Boundary conditions are conditions that specify the values of the solution at certain points or boundaries. They are important because they help determine the constants of integration and provide a unique solution to the differential equation.

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