To find the derivative of cot(x), we start by using the quotient rule:
(cot x)’ = [(cos x)^(-1)]’
= -1(cos x)^(-2)(-sin x)
= sin x/(cos x)^2
= sin x/cos^2(x)
= sin x sec^2(x)
Therefore, the derivative of cot(x) is -sin(x)/sin^2(x) or -csc^2(x).
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