How do you find the derivative of (6 csc x)/x?

Answer 1

[ low*d(high) - high*d(low) ] / (low)^2
where
high = numerator
low = denominator
d(high) and d(low) = respective derivatives

first recall that the derivative of csc x = -(cot x)(csc x)
therefore,
[ x*(-6 (cot x)(csc x)) - 6 (csc x) ]/x^2
or
-(6 csc x)*(x(cot x) + 1)/x^2

hope this helps~ :)