Deriving the Derivative Formula for Inverse of sinx on [-pi/2,pi/2]?

[kathrynag]

Homework Statement

Use Inverse Function Thm to derive the formula for the derivative of the inverse of sinx on the interval [-pi,2,pi/2]

Homework Equations

f^-1(f(x))=1/f'(x)

The Attempt at a Solution

1/cosx

 

[Mark44]

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).

 

[Mark44]

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.

 

[kathrynag]

Never mind I figured it out.