Derivative of cot(x)
-csc^2u du
The derivative of cot(x) can be found using the quotient rule of differentiation as follows:
Let y = cot(x)
Using the identity, cot(x) = cos(x) / sin(x)
y = cos(x) / sin(x)
Taking the derivative of y with respect to x:
y’ = [(cos(x) * sin (x)) – (sin(x) * (-sin(x)))] / sin^2(x)
Simplifying the above expression:
y’ = [cos(x) * sin(x) + sin^2(x)] / sin^2(x)
y’ = cos(x)/sin(x) + sin(x)/sin^2(x)
y’ = cot(x) + csc^2(x)
Therefore, the derivative of cot(x) is -csc^2(x).
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