To find the derivative of cot(x), we will use the quotient rule:
cot(x) = cos(x) / sin(x)
Using the quotient rule, we can find the derivative as:
cot'(x) = [sin(x)*(-sin(x)) – cos(x)*cos(x)] / [sin(x)]^2
Simplifying this expression by using the trigonometric identity sin^2(x) + cos^2(x) = 1, we can express the derivative as:
cot'(x) = -[1 + cot^2(x)]
Therefore, the derivative of cot(x) is -[1 + cot^2(x)].
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