To find the derivative of cot(x), we can use the quotient rule:
Let u = cos(x) and v = sin(x):
cot(x) = cos(x) / sin(x)
= u / v
Using the quotient rule, the derivative of cot(x) is:
d/dx(cot(x)) = (v d/dx(u) – u d/dx(v)) / v^2
= (-sin(x) – cos(x)sin(x)) / sin^2(x)
= – (sin(x) + cos(x)sin(x)) / sin^2(x)
= – (1 + cos(x)) / sin^2(x)
Therefore, the derivative of cot(x) is:
d/dx(cot(x)) = – (1 + cos(x)) / sin^2(x)
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