Differential
A differential is a representation of an infinitesimally small change.
Contents
Description
Given a function f(x), the differential of the function can be expressed in terms of the differential of x: df = f' dx. Note that while f' can also be expressed as df/dx, that notation can mislead one to believing it is a trivial equality. The dx in the derivative cannot be 'cancelled out' by multiplying against the differential of x.
Note also that this equation holds only for infinitesimally small changes. For an observable change in x, notated as Δx, the corresponding change in f can only be approximated as Δf ≈ f' Δx.
Given a multivariate function f(x, y, z), the total differential is expressed as df = fxdx + fydy + fzdz where
fx = ∂f/∂x
fy = ∂f/∂y
fz = ∂f/∂z