Math (Calculus)

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this is a question I don't understand:

Demonstrate the following derivative rule:

(Arccsc(u))' = (-1/u(u^2-1)^1/2) * u'

Where u = g(x)

Do they want me to start with (Arccsc(u)) and get to (-1/u(u^2-1)^1/2) * u' ?

Thank you

  • Math (Calculus) -

    That's the idea, but you have to go to it backwards, in a way

    if y = arccsc(x) then x = csc(y)

    dx/dy = -cscy ctny

    but ctny = sqrt(csc^2 y - 1)

    dx/dy = -x sqrt(x^2 - 1)

    dy/dx = -1/[x * sqrt(x^2-1)]

    If we have y = arccsc(u) then the chain rule says we have

    dy/dx = dy/du * du/dx = -1/[u * sqrt(u^2-1)]
    du/dx

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