Can't remember how to differentiate this

In summary, the conversation is about finding the second derivative of Axe^(-x^2/ L^2) for a Schrodinger equation. The person asking for help is struggling with the solution and is missing the chain rule and product rule. They are advised to review first-year calculus before attempting to solve the equation.
  • #1
rainbojedi
2
0
for my Schrodinger equation I need the second derivative of this: Axe^(-x^2/ L^2)
I think that I am missing some chain rule or something.



The solutions say: ( 4Ax^3-6AxL^2)(1/L^4)e^(-x^2/ L^2)


I only got -2Axe^(-x^2/L^2) for the 1st deriv. and 4Axe^(-x^2/L^2) and I still can't figure out what I'm missing even by looking at the solutions.
 
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  • #2
I think you are missing both the product rule and the chain rule. I'm not even sure what rule you are using. Warm up by taking the derivative of x*exp(-x^2). You should get exp(-x^2)-2*x^2*exp(-x^2). I think you may need to crack a first year calc text before dealing with the SE.
 
  • #3
Your first derivative is immediately wrong because you didn't use the product rule (but you also forgot chain rule).
 
  • #4
Thank you, your were both very right. I had immediately missed the product rule. Thanks for the help. :redface:
 
Last edited:

FAQ: Can't remember how to differentiate this

How do I differentiate this expression?

Differentiation is a mathematical process of finding the rate of change of a function with respect to its independent variable. In order to differentiate an expression, you need to use the rules of differentiation, such as the power rule, product rule, quotient rule, and chain rule.

What if I can't remember the differentiation rules?

If you can't remember the differentiation rules, you can refer to a math textbook or online resources for a quick review. It's also helpful to practice differentiating various types of expressions to improve your understanding and memory of the rules.

Can I use a calculator to differentiate an expression?

Yes, there are many online calculators and graphing calculators that can differentiate expressions for you. However, it's important to understand the rules of differentiation and not solely rely on a calculator.

How do I know which rule to use when differentiating an expression?

The rule you use to differentiate an expression depends on the type of function and the operations involved. For example, if the expression contains only variables and constants, you can use the power rule. If it involves multiplication or division, you can use the product or quotient rule. And if it contains nested functions, you can use the chain rule.

Is there a shortcut to differentiate expressions?

While there are some shortcuts that can be used in specific cases, such as the shortcut for differentiating logarithmic and exponential functions, it's important to understand and apply the differentiation rules correctly. This will ensure accurate results and a deeper understanding of the concept.

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