Question

If \[y=\sin^{-1}x\], what is \[\frac{dy}{dx}\]?

Options

• \[\frac{1}{1-x^2}\]

• \[\frac{1}{\sqrt{1-x^2}}\]

• \[\sqrt{1-x^2}\]

• \[-\frac{x}{\sqrt{1-x^2}}\]

Answer 1

The first derivative of \[\sin^{-1}x\] is \[\frac{1}{\sqrt{1-x^2}}\]. This may equivalently be written as \[\sqrt{1-x^2}\frac{dy}{dx}=1\].