Posted by Zukii on Tuesday, March 8, 2011 at 9:20pm.
Use the chain rule: d(ln(√sin(x)))/dx =[1/(√sin(x))]*d√(sin(x))/dx =[1/(√sin(x))]*[1/(2√(sin(x)))]*d(sin(x))/dx =[1/(√sin(x))]*[1/(2√(sin(x)))]*cos(x)