With respect to waves traveling through a diffraction grating, we have an equation like this one: $$d_s\sin(\theta) = m\lambda.$$
Where $d_s$ is the distance between slits in the grating, $\theta$ is an approximate angle at which the waves bend through each slit of the grating, $\lambda$ is the wavelength of the waves passing through the gradient, and $m$ is the number of wavelengths by which distances traveled by one wave from one slit differ from an adjacent slit. $d_s$ and $m$ are usually given a remain constant in the scenarios I'm working with.
My physics book says that the differential of the above mentioned equation is $$d_s \cos(\theta)d\theta = md\lambda$$ (without confusing the single $d_s$ (distance) with the ones in $d\theta$ and $d\lambda$).
What does it mean to call the second equation the "differential" of the first? I am trying to understand the concept behind the differentials more so that I may later make sense of the physics.
EDIT: In user6786's question, user6786 states that "according to the formula $dy=f'(x)dx$ we are able to plug in values for $dx$ and calculate a $dy$ (differential)". I'm trying to see how that works.