Question

Find the derivative of log[cot[pi/4+x/2]]

Answer 1

let y = log[cot[$\pi /4 + x/2$

dy/dx = [1/cot($\pi /4 + x/2$)] * (- cosec²($\pi /4 + x/2$)) * (1/2)
 [by chain rule] 

dy/dx = - cosec($\pi /4 + x/2$) * sec ($\pi /4 + x/2$) / 2