Question

How do you differentiate `f(x) =arcsin(2x + 1)`?

Answer 1

It is `f'(x)=2/(sqrt(1-(2x+1)^2))`

Explanation:

Let `u(x) = 2x + 1`, function f may be considered as the composition `f(x) = arcsin(u(x))`. Hence we use the chain rule,
`f '(x) = ((du)/dx) (d(arcsin(u)))/(du)`,
to differentiate function f as follows

`f'(x)=((2x+1)/dx)*(1/(sqrt(1-u^2))) => f'(x)=2/(sqrt(1-(2x+1)^2))`