Question

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

Answer 1

`d/dxsin^(-1)(x/2)=1/(2(sqrt(1-(x^2/4)))`

Explanation:

The rule for differentiation of the inverse sine function states that :

`d/dx sin^(-1)u(x)=1/(sqrt(1-u^2))*(du)/dx`.

So applying this rule in this particular case we get :

`d/dxsin^(-1)(x/2)=1/(sqrt(1-(x/2)^2))*(1/2)`