Derivative of cot(x)
To find the derivative of cot(x), we can use the chain rule
To find the derivative of cot(x), we can use the chain rule. The cotangent function is defined as the reciprocal of the tangent function, so we can rewrite it as cot(x) = 1/tan(x).
Using the quotient rule, the derivative of the cotangent function is:
d/dx [cot(x)] = d/dx [1/tan(x)]
= (tan(x) * d/dx [1] – 1 * d/dx [tan(x)]) / (tan(x))^2
= (-sec^2(x) * d/dx [tan(x)]) / (tan(x))^2
Now, we need to find the derivative of the tangent function. The derivative of tangent function is sec^2(x). So, substituting this value, we get:
= (-sec^2(x) * sec^2(x)) / (tan(x))^2
= -sec^4(x) / tan^2(x)
Therefore, the derivative of cot(x) is -sec^4(x) / tan^2(x).
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