Derivative of Cot
d/dx cot(x) = -csc²(x)
The derivative of cot function can be found using the quotient rule of differentiation. Let y = cot(x), then
y = cos(x) / sin(x)
Using the quotient rule, we have
y’ = [ sin(x) (-sin(x)) – cos(x) cos(x) ] / sin^2(x)
simplifying,
y’ = – [cos^2(x) + sin^2(x)] / sin^2(x)
y’ = -1 / sin^2(x)
Therefore, the derivative of cot(x) is -csc^2(x), where csc(x) = 1/sin(x).
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