In my financial derivatives class, I am confused by the meaning of the d's in the following equation. Are they derivatives? What are they?
dLt = mdt + σdBt
Where L = log(St), log return
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People in probability and finance theory to use this notation to write integral equations describing the behavior of continuous time stochastic processes (L, in this case). It's an informal shorthand way of writing an equation that otherwise would have cumbersome (and scary looking) integral signs in front of everything.
In other words, to see what it really means, write an integral sign in front of everything.
Take a look at the wikipedia section I linked. Based on the way you asked the question, it sounds like you may need to read a primer on stochastic calculus before you will have a reasonable understanding of an equation like this.
It's a stochastic differential equation (SDE) and d's are notation used in differential calculus. The derivatives (Mathematics not the financial ones like IFRS 9). To understand SDE, first try to understand ordinary differential equations (ODE), Probability theory and number theory, Linear algebra, Real analysis etc