A question about notation on derivatives

In summary, the conversation discusses a question about notation in a problem involving a Lagrangian and a transformation. The notation in question is the "total derivative", which is written as \frac{\delta L}{\delta \lambda} and is equivalent to \frac{\partial L}{\partial x}\frac{dx}{d\lambda}+ \frac{\partial L}{\partial y}\frac{dy}{d\lambda} by the chain rule. This notation is commonly used in physics texts.
  • #1
atomqwerty
94
0
Hi,
I didn't put this into homework since is only a question about notation:

In a problem, given a Lagrangian and a transformation (x,y) -> (x',y'), where these x' and y' depend on λ, in particular like [itex]e^{\lambda}[/itex]. The problem asks for the derivative [itex]\frac{\delta L}{\delta \lambda}[/itex]. What this notation corresponds to? Thanks
 
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  • #2
That is the "total derivative",
[tex]\frac{\delta L}{\delta \lambda}= \frac{\partial L}{\partial x}\frac{dx}{d\lambda}+ \frac{\partial L}{\partial y}\frac{dy}{d\lambda}[/tex]
by the chain rule.

It more often seen in physics texts than math texts. Math texts would just us "[itex]dL/d\lambda[/itex]".
 

1. What exactly is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function with respect to its independent variable. It is often interpreted as the slope of the tangent line to a function at a particular point.

2. How is a derivative notated?

The most common notation for a derivative is the 'prime' notation, where the derivative of a function f(x) is represented as f'(x). Other notations include using the symbol D or the Leibniz notation of dy/dx.

3. What is the purpose of taking derivatives?

Derivatives are used to analyze the behavior of functions and understand their rates of change. They have many practical applications in fields such as physics, economics, and engineering.

4. Are there any rules or formulas for finding derivatives?

Yes, there are several rules and formulas for finding derivatives, such as the power rule, product rule, quotient rule, and chain rule. These rules make it easier to find the derivative of more complex functions.

5. Can derivatives be negative?

Yes, derivatives can be positive, negative, or zero. A positive derivative indicates that the function is increasing, a negative derivative indicates that the function is decreasing, and a zero derivative indicates that the function has a stationary point.

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