# Inverse Function Theorem

1. Dec 16, 2008

### kathrynag

1. The problem statement, all variables and given/known data
Use Inverse Function Thm to derive the formula for the derivative of the inverse of sinx on the interval [-pi,2,pi/2]

2. Relevant equations
f^-1(f(x))=1/f'(x)

3. The attempt at a solution
1/cosx

2. Dec 16, 2008

### Staff: Mentor

I vaguely remember a formula something like the one you show, but I think you have it wrong. f^(-1)(f(x)) on the left side would simplify to just plain x, and I don't see how that would be equal to 1/f'(x).

3. Dec 16, 2008

### Staff: Mentor

Or maybe not...

Try this:
y = sin^(-1)(x) $$\iff$$ x = sin(y)
Now differentiate implicitly with respect to x, getting
1 = cos(y) * dy/dx

Solve for dy/dx, and in the resulting expression, replace y with what it's equal to.

4. Dec 16, 2008

### kathrynag

Never mind I figured it out.