A question about notation on derivatives

[atomqwerty]

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 $e^{\lambda}$. The problem asks for the derivative $\frac{\delta L}{\delta \lambda}$. What this notation corresponds to? Thanks

 

[HallsofIvy]

That is the "total derivative",
$$\frac{\delta L}{\delta \lambda}= \frac{\partial L}{\partial x}\frac{dx}{d\lambda}+ \frac{\partial L}{\partial y}\frac{dy}{d\lambda}$$
by the chain rule.

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