Question

What is the derivative of `arcsin(x^2/4)`?

Answer 1

`d/dx(arcsin(x^2/4)) = x/(2sqrt(1-x^4/16))`

Explanation:

Let `u=x^2/4`

`d/dx(arcsinu) = 1/sqrt(1-u^2) * d/dx(u)`

`d/dx(u) = x/2`

The rest is just plugging in and multiplying `u`.