derv cot(x)
To find the derivative of cot(x), we can use the quotient rule
To find the derivative of cot(x), we can use the quotient rule.
The quotient rule states that for two functions u(x) and v(x), the derivative of their quotient is given by:
(d/dx)(u(x)/v(x)) = (v(x)(du/dx) – u(x)(dv/dx)) / (v(x))^2
In this case, u(x) = 1 and v(x) = tan(x).
Since the derivative of u(x) is 0 (a constant), we only need to find the derivative of v(x), which is:
(d/dx)tan(x) = sec^2(x)
Now let’s plug the values into the quotient rule formula:
(d/dx)(cot(x)) = (tan(x)(0) – 1(sec^2(x))) / (tan^2(x))
Simplifying further, we have:
(d/dx)(cot(x)) = -sec^2(x) / tan^2(x)
Since sec^2(x) is equal to 1 + tan^2(x) (a trigonometric identity), we can rewrite the derivative as:
(d/dx)(cot(x)) = -1 / sin^2(x)
So, the derivative of cot(x) is -1 / sin^2(x).
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