Derivative of cot x
-csc^2 x
The derivative of cot(x) can be found by using the quotient rule of differentiation.
cot(x) = cos(x)/sin(x)
Using the quotient rule:
(d/dx) cot(x) = [(sin(x) * (-sin(x))) – (cos(x) * cos(x))] / (sin(x))^2
Simplifying this expression:
(d/dx) cot(x) = (-sin^2(x) – cos^2(x)) / (sin^2(x))
Recall that sin^2(x) + cos^2(x) = 1, we can simplify further:
(d/dx) cot(x) = -1 / (sin^2(x))
Therefore, the derivative of cot(x) is:
(d/dx) cot(x) = -csc^2(x)
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