What is the derivative of [cot x]
-csc^2 x
To find the derivative of [cot x], we need to use the quotient rule.
Recall that the cotangent function is defined as cos(x)/sin(x), so we can rewrite [cot x] as [cos(x)/sin(x)].
Now, using the quotient rule, we can find the derivative of [cot x] as follows:
[d/dx]([cos(x)/sin(x)]) = [(sin(x) * (-sin(x))) – (cos(x) * cos(x))] / sin(x)^2
Simplifying this expression, we get:
[d/dx]([cot x]) = (-sin^2(x) – cos^2(x)) / sin^2(x)
Recall that sin^2(x) + cos^2(x) = 1, so we can simplify the derivative to:
[d/dx]([cot x]) = -1 / sin^2(x)
Therefore, the derivative of [cot x] is -csc^2(x).
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