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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