Why is the statement false?

Question

If x=f^-1 (y) (meaning y= f(x)), then (dy/dx) = -(f(y))^-2 f '(y)

Answer 1

In the condition the -1 is used to denote and represent the INVERSE function,

but then in the conclusion, the meaning of the -1 changes to denote and represent

the EXPONENT. So the meaning changes from one part to the next.

Here is an easy counter example:

y = x <--- the identity function

x = y <--- the inverse

The derivative of the original function is y'=1

which equals the derivative of the inverse, 1 = y'

But in the statement, the derivative is supposed to be

-1*y' = 1 --> y' = -1 which is false

since this silly and ridiculous statement fails for y=x, it

will certainly fail for more complicated functions.