Math (Calculus)
posted by Jim on .
this is a question I don't understand:
Demonstrate the following derivative rule:
(Arccsc(u))' = (1/u(u^21)^1/2) * u'
Where u = g(x)
Do they want me to start with (Arccsc(u)) and get to (1/u(u^21)^1/2) * u' ?
Thank you

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^21)]
If we have y = arccsc(u) then the chain rule says we have
dy/dx = dy/du * du/dx = 1/[u * sqrt(u^21)]
du/dx