d/dx csc(x)
To find the derivative of csc(x), we can use the quotient rule
To find the derivative of csc(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 the formula:
(d/dx)(u(x) / v(x)) = (v(x) * u'(x) – u(x) * v'(x)) / (v(x))^2
In this case, u(x) = 1 and v(x) = sin(x). Therefore, we have:
(d/dx)(csc(x)) = (sin(x) * 1 – 1 * cos(x)) / (sin(x))^2
Simplifying the expression, we get:
(d/dx)(csc(x)) = (sin(x) – cos(x)) / (sin(x))^2
So, the derivative of csc(x) is (sin(x) – cos(x))/ (sin(x))^2.
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