essential thing is that we can use differentials to understand
  and approximate how small changes in the inputs of a function
  will change the outputs of the function. For example, we can
  approximate the change in a function $f(x,y)$ if we know how much
  $x$ and $y$ will change.</p>
    <p>Using differentials to analyze how outputs of a function change
    when the inputs change comes up in many applications, such as
    analyzing numerical roundoff error in calculations or analyzing
    manufacturing 