I am studying calculus at home as a hobby. I have 2 books: The Complete Idiot's Guide to Calculus by W. M. Kelley (K), and Calculus Made Easy (1998)by S.P.Thomson and M.Gardner (T).

On page 119 of (K) a formula is derived which seems to show that the derivative of the inverse function equals the reciprocal of the derivative of the inverse function! This is contradicted by (T) page 148: "...the reciprocal of the derivative of the inverse function gives the derivative of the function itself. The latter version seems to me to be correct, but I cannot see where the other version goes wrong when it is produced in the "Critical Point " box on p119 of (K).

It may be that I am missing the point because of the 2 different notations which are being used. Unfortunately I cannot access on my webpage any maths symbols, hence the description above. I would be grateful for an explanation of my problem and also some advice as to how I access maths symbols.