How do you differentiate #f(x)=sqrt(cot(x)) # using the chain rule?
1 Answer
Feb 3, 2016
#f'(x) =( -cosec^2x)/(2sqrtcotx #
Explanation:
note
# (d/dx(cotx) = -cosec^2x )# rewrite f(x) as
#f(x) = (cotx)^(1/2) # differentiate using
#color(blue)(" chain rule ")#
# f'(x) = 1/2(cotx)^(-1/2) d/dx(cotx) #
# = 1/2(cotx)^(-1/2) . (-cosec^2x) # 'tidying up' to obtain
#f'(x) =( -cosec^2x)/(2sqrtcotx) #
