Differentiating Logarithmic Functions without Base e
Key Questions

By Change of Base Formula:
#log_bx={log_ax}/{log_ab}# ,#y=log_3x={lnx}/{ln3}# By taking the derivative,
#y'={1/x}/{ln3}=1/{(ln3)x}# 
Answer:
#tan(x)/ln(2)# Explanation:
#f(x)=log_2(cos(x))=ln(cos(x))/ln(2)# #1/ln(2)# is just a constant and can be ignored.#(ln(u))'=(u')/u# #u=cos(x), u'=sin(x)# #f'(x)=1/ln(2)*(sin(x))/cos(x)=tan(x)/ln(2)# 
Change of Base Formula
#log_bx={log_ax}/{log_ab}# ,where
#a# is any positive number except#1# .I hope that this was helpful.