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

1 Answer
Mar 23, 2017

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).