Derivative cotx
The derivative of cot(x), denoted as d/dx (cot(x)), represents the rate of change of the cotangent function with respect to the variable x
The derivative of cot(x), denoted as d/dx (cot(x)), represents the rate of change of the cotangent function with respect to the variable x. To calculate the derivative of cot(x), we can use the quotient rule.
The cotangent function can be defined as cot(x) = 1 / tan(x), where tan(x) is the tangent function.
Let’s use the quotient rule to find the derivative:
1. Start by differentiating the numerator and the denominator of the fraction separately.
– The derivative of 1 is 0.
– The derivative of tan(x) is sec^2(x), where sec(x) is the secant function.
2. Apply the quotient rule:
– (0 * tan(x) – 1 * sec^2(x)) / (tan(x))^2
3. Simplify the expression further:
– (-sec^2(x)) / (tan(x))^2
Now, we have the derivative of cot(x) as -sec^2(x) / (tan(x))^2. This can also be written as -cos^2(x) / sin^2(x) or -cos^2(x) * csc^2(x).
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