Question

deriv of y=sin^-1 Sqrt of 1-u^2

Answer 1

\[\Large y\quad=\quad \arcsin\left(\color{royalblue}{x}\right)\]Hmmm, do you remember this derivative?

Answer 2

\[\Large y'\quad=\quad \arcsin\frac{1}{\sqrt{1-(\color{royalblue}{x})^2}}\]Our problem will work out similar to this, but we'll have to remember the chain rule.

Answer 3

\[\Large y\quad=\quad \arcsin\left(\color{royalblue}{\sqrt{1-u^2}}\right)\]\[\Large y'\quad=\quad \frac{1}{\sqrt{1-\left(\color{royalblue}{\sqrt{1-u^2}}\right)^2}}\left(\color{royalblue}{\sqrt{1-u^2}}\right)'\]

Answer 4

So chain rule tells us to multiply by the derivative of the inner function.
What's the derivative of \(\Large \sqrt{1-u^2}\) ?