^{-1}(x), the inverse of f(x). He knows the following derivative rules.

1. The Sum Rule: the derivative of (f+g)(x)=f(x)+g(x)

(f+g)'(x)=f'(x)+g'(x)

2. The Product Rule: the derivative of fg(x)=f(x)g(x)

(fg)'(x)=f'(x)g(x)+f(x)g'(x)

3. The Chain Rule: the derivative of (f*g)(x)=f(g(x))

(f*g)'(x)=f'(g(x))g'(x)

How can David find the Inverse Rule? What is the derivative of f^{-1}(x)?