Learn To Find The Derivative Of Cot(X) Using The Quotient Rule Of Differentiation

d/dx cotx

derivative of cot(x) is -cosec^2(x) or -1/[sin(x)*cos^2(x)].

To find the derivative of cot(x), we can use the quotient rule of differentiation, since cot(x) is formed by dividing cosine and sine functions.

Quotient rule: (f/g)’ = (f’g – g’f)/g^2

So, let f(x) = 1 and g(x) = tan(x)

cot(x) = f(x)/g(x) = 1/tan(x) = cos(x)/sin(x)

Now differentiate cot(x) using the quotient rule:

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

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

= [(-sin(x)sin(x) – cos(x)cos(x))/sin^3(x)] / (tan^2(x))

= -1/[sin(x)*cos^2(x)]

Therefore, the derivative of cot(x) is -cosec^2(x) or -1/[sin(x)*cos^2(x)].

Hence, d/dx cot(x) = -cosec^2(x) or -1/[sin(x)*cos^2(x)].

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