using chain rule or inverse function rule, how can you prove that sin^-1 x is equal to 1/(sqrt(1-x^2))
The best way to do it is to use right triangles. Start with this info.Originally Posted by jonny4407
$\displaystyle \sin^{-1}(x)=y$
So, taking the sine of both sides gives us that $\displaystyle \sin(y)=x$
Draw a triangle with y as the angle, and make the sine of y equal to x. Differentiate both sides of you equation, and solve for $\displaystyle \frac{dy}{dx}$.
Good luck.