y a small change in the input $x$. In other words,
    if the input $x$ changes by a small amount $dx$, then we
    multiply that small change by the derivative to determine how
    much $y$ changes (i.e., $dy$).
  </blockquote>
    <p>To get the derivative in all dimensions, we just substitute
  in vectors to obtain the differential notation $d\vec y = f'(\vec
  x) d\vec x$. The derivative is precisely the thing that tells us
  how to get $d\vec y$ from $d\vec x$. We'll quickly see that the
  derivative $f