Derivative of function

  • Thread starter kmeado07
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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.
 

Answers and Replies

  • #2
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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 [itex]\pi[/itex] is pi, not pie.
 

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