How to Find the Derivative of cot(x) Using the Quotient Rule: Step-By-Step Guide for Math Enthusiasts

cot(x)’ =

To find the derivative of cot(x), we can use the quotient rule

To find the derivative of cot(x), we can use the quotient rule.

The cotangent function can be written as cos(x)/sin(x).

Let y = cot(x).
Then, we can rewrite cot(x) as y = cos(x)/sin(x).

Using the quotient rule, the derivative of cot(x) is given by:

dy/dx = (sin(x)(-sin(x)) – cos(x)(cos(x))) / (sin(x))^2

Simplifying the expression, we get:

dy/dx = (-sin^2(x) – cos^2(x)) / sin^2(x)

Using the trigonometric identity sin^2(x) + cos^2(x) = 1, we can simplify further:

dy/dx = (-1) / sin^2(x)

Thus, the derivative of cot(x) is:

dy/dx = -csc^2(x), where csc(x) represents the cosecant function (1/sin(x)).

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