Let $k$ be a constant. Compute $\frac{d}{dx}[ \ln (kx) ]$ in two ways.

1. Using the Chain Rule, first decompose $y = \ln(kx)$ into an outside and inside function.
   Outside function (in terms of $u$): $y =$
   Inside function (in terms of $x$): $u =$
   Then find the derivative, $\frac{d}{dx}[ \ln (kx) ] =$ (simplify your answer).
2. Using a law of logarithms to simplify first:
   $\ln(kx) =$ ? + - * / $\ln x$ (Fill in the blanks to make this a true statement.)
   Now take the derivative of the simplified function: $\displaystyle{\frac{dy}{dx} = }$