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

Question

1380 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-19T17:33:50

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

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 :

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

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