Derivative of Arcsine Function
- Tim Brzezinski
For the function , notice how y is written in terms of x. Rewrite this equation so that x is written in terms of y.
For the equation you wrote in (1) above, use implicit differentiation to differentiate both sides of your equation with respect to x.
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.
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?