Derivatives of Scalar Multiples 
 
      Why
 Is some scaled form of a differentiable
  function differentiable?
Result
 Suppose $I \subset \R $ is an interval and $f:
  I \to \R $ is differentiable.
 Then given any real number $\lambda  \in \R $,
  the function $\lambda g$ is a differentiable
  functions whose derivative is $\lambda g'$.