Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.1 Exercises - Page 325: 63

$y'=\frac{tan(x)}{cos(x)-1}$

$y=ln|\frac{cos(x)}{cos(x)-1}|$ $=ln(cos(x)-ln(cos(x)-1)$ $y’=\frac{-sin(x)}{cos(x)}-\frac{-sin(x)}{(cos(x)-1)}$ $=-\frac{sin(x)}{cos(x)}=\frac{sin(x)}{(cos(x)-1)}$ $=\frac{-(sin(x)cos(x)+sin(x)+(sin(x)cos(x)}{cos(x)(cos(x)-1)}$ $=\frac{sin(x)}{cos(x)(cos(x)-1)}$ $=\frac{tan(x)}{cos(x)-1}$