How do you differentiate #f(x)=sqrt(cot(x)) # using the chain rule?

1 Answer
Feb 3, 2016

Answer:

#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) #