Question

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

Answer 1

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

Explanation:

As a rule: `d/dx[arcsin(u)]=(u')/sqrt(1-u^2)`.

Now just plug in `x/2=u` and you get: `(d/dx[x/2])/sqrt(1-(x/2)^2)`. If we power down we can determine that `d/dx[x/2]=1/2`. Plug this in and we will get `(1/2)/sqrt(1-(x/2)^2)`. If we simply we get `1/(2sqrt(1-x^2/4))` and this is the derivative of `arcsin(x/2)`.