Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.5 Exercises - Page 362: 57

$g'(t)=\frac{10}{\ln4}(\frac{1-\ln t}{t^2})$

$g(t)=\frac{10\frac{\ln t}{\ln4}}{t}$ $g(t)=\frac{10}{ln4}(\frac{lnt}{t})$ $g(t)=\frac{10}{ln4}(lnt)(t^{-1})$ let $u=lnt$ $u'=\frac{1}{t}$ $v=t^{-1}$ $v'=-t^{-2}$ $g'(t)=\frac{10}{ln4}(\frac{1}{t^2}-\frac{lnt}{t^2})$ $=\frac{10}{\ln4}(\frac{1-\ln t}{t^2})$