Derivative of arccsc(x)
-du/abs(u)sqrt(u^2-1)
The derivative of arccsc(x) can be found using the chain rule and the derivative of the inverse function formula.
Let y = arccsc(x), then csc y = x.
Taking the derivative of both sides with respect to x:
csc y * (-csc y cot y) * dy/dx = 1
Simplifying:
dy/dx = -sin y / (csc y * cot y)
Using the identity csc y = 1/sin y and cot y = cos y / sin y:
dy/dx = -sin y / (1/sin y * cos y / sin y)
dy/dx = -sin^2 y / cos y
Substituting csc y = x:
dy/dx = -1/(x*sqrt(x^2 – 1))
Therefore, the derivative of arccsc(x) is -1/(x*sqrt(x^2 – 1)).
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