derivative of cotx
-csc^2x
The derivative of cot(x) can be found using the Quotient Rule of differentiation. Here, cot(x) can be written as cos(x)/sin(x), which can be differentiated as:
[d/dx (cos(x)) * sin(x) – cos(x) * d/dx (sin(x))] / (sin(x))^2
Since d/dx(cos(x)) = -sin(x) and d/dx(sin(x)) = cos(x), the expression simplifies as:
[-sin^2(x) – cos^2(x)] / (sin(x))^2
Using the identity sin^2(x) + cos^2(x) = 1, the expression further simplifies as:
-1 / (sin(x))^2
Therefore, the derivative of cot(x) is -csc^2(x).
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