The derivative of cotx with respect to x can be found using the quotient rule:
cotx = cosx / sinx
(d/dx) cotx = (d/dx) (cosx / sinx)
= [ (sinx) (-sinx) – (cosx) (cosx) ] / (sinx)^2
= – [ cos^2(x) + sin^2(x) ] / (sinx)^2
= -1 / (sinx)^2
Therefore, the derivative of cotx with respect to x is equal to -1 / (sinx)^2.
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