Posted by Ryan on September 04, 2002 at 12:34:44:
In Reply to: inverse derivative posted by Ryan on August 30, 2002 at 09:05:02:
I solved it: subbing f(g(x)) and g(f(x)) and using y'=1/x' --> My faulty logic was that I could sub U for x' but then I assumed I could just make y' y". I didnt use the given info--> that y is a func of x and x is a func of y.
: x=g(x) is the inverse of y=f(x)
: does d2y/dx2 = 1/(d2x/dy2)?
: sugg: g' is a function of x and x is a function of y
: find the derivative of y'=1/x' with respect to x, and use the chain rule on the right side.
: I make U=x' and du = x", so i get x"(-1/x'^2)
: --> The answer is y"=-x"/(x'^3) --> but I am only getting y"=-x"/(x'^2)
: What am I missing????
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