Answer
$$g'\left( x \right) = 4 - \frac{7}{x}$$
Work Step by Step
$$\eqalign{
& g\left( x \right) = 4x - 7\ln x \cr
& {\text{Calculate the derivative of the function}} \cr
& g'\left( x \right) = \frac{d}{{dx}}\left( {4x} \right) - \frac{d}{{dx}}\left( {7\ln x} \right) \cr
& {\text{Drop out the constants}} \cr
& g'\left( x \right) = 4\frac{d}{{dx}}\left( x \right) - 7\frac{d}{{dx}}\left( {\ln x} \right) \cr
& {\text{Compute derivatives}}{\text{, }} \cr
& g'\left( x \right) = 4\left( 1 \right) - 7\left( {\frac{1}{x}} \right) \cr
& g'\left( x \right) = 4 - \frac{7}{x} \cr} $$
