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)

More Answers:

[next_post_link]

Share:

Recent Posts

Mathematics in Cancer Treatment

How Mathematics is Transforming Cancer Treatment Mathematics plays an increasingly vital role in the fight against cancer mesothelioma. From optimizing drug delivery systems to personalizing

Read More »