Derivative of Cot
The derivative of the cotangent function (Cot) can be found using the quotient rule
The derivative of the cotangent function (Cot) can be found using the quotient rule.
Let’s consider the cotangent function as the ratio of the cosine function (cos) and the sine function (sin), i.e., Cot(x) = cos(x)/sin(x).
To find the derivative of the cotangent function, we need to find the derivative of both the numerator (cos(x)) and the denominator (sin(x)) separately using the chain rule and then apply the quotient rule.
The derivative of cos(x) is -sin(x) and the derivative of sin(x) is cos(x).
Now, applying the quotient rule:
(d/dx) [Cot(x)] = ( [-sin(x)] * sin(x) – cos(x) * cos(x) ) / [sin(x)]^2
= -sin^2(x) – cos^2(x) / sin^2(x)
= -[1 / sin^2(x)]
= -csc^2(x)
Therefore, the derivative of the cotangent function (Cot(x)) is -csc^2(x), where csc(x) represents the cosecant function.
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