Question

What's the derivative of `f(x) = arctan[x/(sqrt(5-x^2))]`?

Answer 1

`1/sqrt(5-x^2)`

Explanation:

Let `x = sqrt5sint`. Then,

`f =arctan(tant)=t=arcsin(1/sqrt5x)`. So,

`f'=1/sqrt(1-x^2/5)(x/sqrt5)'`

`=sqrt5/(sqrt(5-x^2))(1/sqrt5)=1/sqrt(5-x^2)`