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How do you find the derivative of ##cotx##?
##dy/dx = -csc^2x##
##y = cotx##
##y = 1/tanx##
##y = 1/(sinx/cosx)##
##y = cosx/sinx##
Letting ##y= (g(x))/(h(x))##, we have that ##g(x) = cosx## and ##h(x) = sinx##.
##y' = (g'(x) xx h(x) - g(x) xx h'(x))/(h(x))^2##
##y' = (-sinx xx sinx - (cosx xx cosx))/(sinx)^2##
##y' = (-sin^2x - cos^2x)/(sinx)^2##
##y' = (-(sin^2x + cos^2x))/sin^2x##
##y' = -1/sin^2x##
##y' = -csc^2x##
Hopefully this helps!