Differentials: Errors and Approximation

Let y = f(x) be a differentiable function. Then the quantities dx and dy are called differentials. The differential dx is an independent variable that is dx can be given any real number as the value. The differential dy is then defined in terms of dx by the relation

dy = f′(x) dx (dx ≈ ∆x)

The differentials dx and dy are both variables, but dx is an independent variable, where as dy is a dependent variable - it depends on the values of x and dx. If dx is given a specific value and x is taken to be some specific number in the domain of f, then the numerical value of dy is determined.