Derivative of sin^-1(x) on Interval [1,-1] with Solution Attempt

[kmeado07]

Homework Statement

Compute the derivative of the following function.

Homework Equations

f:[1,-1] arrow [-pie/2, pie/2] given by f(x)=sin^-1 (x)

The Attempt at a Solution

I know that f ' (x)=1/[sqrt(1-x^2)]

Im not sure how to include the intervals of pie given, not sure what they want me to do.

 

[Mark44]

Knowing what the derivative is doesn't do you much good if you have compute it.

Do you know about implicit differentiation?

If so, letting y = f(x), you have y = sin^-1(x)
Solve this equation for x, and then calculate dy/dx.

When you do this, you should get dy/dx = 1/cos(sin^-1(x)), which you can simplify further. That's where the interval [-pi, pi] comes into play.

BTW, the name of the Greek letter \pi is pi, not pie.