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Vito Prosciutto: Teaching community college math on the road to a PhD.

Friday, October 22, 2004

17:19
Princeton Review: Cracking the GRE Math Test 

Aha, I finally figured out the difficulty with the derivative of an inverse function that was offered in the Princeton review book. I had thought that the book had offered:
(f-1)'(y0)=1/f'(y0)
But in fact, it was
(f-1)'(y0)=1/f'(x0)
Aha, and given that y0=f(x0) (or more, to the point x0=f-1(y0), then we really have
(f-1)'(y0)=1/f'(f-1(y0))
which explains why the derivative of arcsin x is actually 1/sqrt(1-x2)

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