# [SOLVED] DERIVATIVE OF sin^-1 x

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• Oct 30th 2005, 05:10 AM
jonny4407
[SOLVED] DERIVATIVE OF sin^-1 x
using chain rule or inverse function rule, how can you prove that sin^-1 x is equal to 1/(sqrt(1-x^2))
• Oct 30th 2005, 06:58 AM
Jameson
Quote:

Originally Posted by jonny4407
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.

$\sin^{-1}(x)=y$

So, taking the sine of both sides gives us that $\sin(y)=x$

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 $\frac{dy}{dx}$.

Good luck.