What is the derivative of cot(x)?
-csc^2(x)
The derivative of cot(x) can be found using the quotient rule of differentiation.
We know that cot(x) can be written as cos(x) / sin(x). Hence,
(d/dx) cot(x) = (d/dx) [cos(x) / sin(x)]
= [sin(x) (-sin(x)) – cos(x) cos(x)] / sin^2(x)
= -[sin^2(x) + cos^2(x)] / sin^2(x)
= -1 / sin^2(x)
Therefore, the derivative of cot(x) is -csc^2(x), where csc(x) represents the cosecant function.
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