How to Find the Derivative of Cot(x) Using Quotient Rule – Step by Step Guide

deriv of cotx

csc squared x

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

(cot x)’ = [(cos x)'(sin x) – (sin x)'(cos x)] / (sin x)^2

Now, (cos x)’ = -sin x and (sin x)’ = cos x. Substituting these into the above equation, we get:

(cot x)’ = [(-sin x)(sin x) – (cos x)(cos x)] / (sin x)^2

Simplifying this expression, we get:

(cot x)’ = (-sin^2 x – cos^2 x) / (sin x)^2

Recall that sin^2 x + cos^2 x = 1, so we can substitute this into the above equation:

(cot x)’ = (-1) / (sin x)^2

Therefore, the derivative of cot(x) is:

(cot x)’ = -csc^2(x)

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