Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - Review Exercises - Page 393: 7

$g'(x) = \frac{1}{2x}$

$g(x) = \ln \sqrt {2x}$ $g(x) = \ln (2x)^{\frac{1}{2}}$ $g(x) = \frac{1}{2}\ln (2x)$ $g'(x) = 0\ln(2x) + (\frac{1}{2})(\frac{1}{2x})(2)$ $g'(x) = (\frac{1}{2})(\frac{1}{2x})(2)$ $g'(x) = \frac{1}{4x}(2)$ $g'(x) = \frac{2}{4x}$ $g'(x) = \frac{1}{2x}$