Differentiation inverse function using Maple

Question

Let $f(x)=2x^2-2,\quad (x \ge 0)$.

Find $\left. \frac{d}{dx}f^{-1}(x)\right|_{x=0}$

Note that $f(1)=0$.

Use $\left. \frac{d}{dx}f^{-1}(x)=\right. \ 1/ f'[f^-{1}(x)]$

Got the answer manually. But how do I key it in Maple?

Answer 1

Examine these steps and see if you agree with them, in terms of what you've learned of the formula for the derivative of the inverse (eg. here).

The equation assigned to R is a substitution for $f^{(-1)}(0)=1$.

restart;
P := diff((f@@(-1))(y),y);
f := x -> 2*x^2-2;
D(f);
P;
eval(P, y=0);
f(1)='f'(1);
R := map(f@@(-1), f(1)='f'(1) );
eval(eval(P, y=0), R);