Derivative of cot(x) with respect to x | -1 / sin^2(x)

d/dx cot x

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

To find the derivative of cot(x) with respect to x, we can use the quotient rule. The quotient rule states that if we have a quotient of two functions, f(x) / g(x), the derivative is given by:

(d/dx)(f(x) / g(x)) = (g(x) * f'(x) – f(x) * g'(x)) / (g(x))^2

In this case, f(x) = 1 and g(x) = tan(x). Therefore, f'(x) = 0 and g'(x) = sec^2(x), where sec(x) represents the secant function.

Using the quotient rule, we can calculate the derivative of cot(x) as:
(d/dx) cot(x) = (tan(x) * 0 – 1 * sec^2(x)) / (tan(x))^2
= -sec^2(x) / tan^2(x)
= -1 / sin^2(x)

So, the derivative of cot(x) with respect to x is -1 / sin^2(x).

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