Question

How do you find the derivative of `(arcsin x)^2`?

Answer 1

Derivative is `(2arcsinx)/sqrt(1-x^2)`

Explanation:

Let us first workout derivative of `arcsinx`. Let `y=arcsinx` i.e. `siny=x` and hence differentiating

`cosy*(dy)/(dx)=1` or `(dy)/(dx)=1/cosy=1/sqrt(1-sin^2y)=1/sqrt(1-x^2)`

Hence `d/(dx)(arcsinx)^2=2arcsinx xx d/(dx)arcsinx`

= `(2arcsinx)/sqrt(1-x^2)`