Question

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

Answer 1

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

Explanation:

The derivative of `arcsinu`:

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

`therefored/dx(arcsin(x/2))=((x/2)')/sqrt(1-(x/2)^2)=(1/2)/sqrt(1-x^2/4)`
`=1/(2sqrt((4-x^2)/4))=1/sqrt(4-x^2)`