# Derivative of Arcsine Function

- Author:
- Tim Brzezinski

- Topic:
- Calculus, Derivative, Sine

Shown below is a graph of the function .
Interact with the applet below for a minute by dragging the white point along the arcsine curve.

**The graph of the derivative of this function will be traced out in gray.**If you'd like, you can take a guess as to what the derivative function might be. (Just don't look it up on another tab.) Hit the**"Clear & Retry"**button to take another guess (if you'd like.) Complete the activity questions that appear below the applet.## 1.

For the function , notice how *y* is written in terms of *x*.
Rewrite this equation so that *x* is written in terms of *y*.

## 2.

For the equation you wrote in (1) above, use implicit differentiation to differentiate both sides of your equation with respect to *x*.

## 3.

Sketch a right triangle that has an acute angle with a measure of "*y".
*Label the 3 sides of this right triangle (in terms of *x*) so that the equation you wrote for (1) is true.

## 4.

Rewrite the expression you obtained in (2) for solely in terms of *x*.
After doing so, enter THIS FUNCTION into the applet above to see how its graph compares with the gray trace.
Is it correct?

**Once you're finished please proceed to the next investigation: Derivative of the Inverse Cosine Function.**