Question

What is the derivative of `y = 23 arctan(sqrt x)`?

Answer 1

`23/(2(sqrt(x))(x+1))`

Explanation:

For this problem, you would use the chain rule. You can pull the 23 "out" to the front as it is a constant multiple. Your setup would look like `23 d/dx arctan(sqrt(x))` . You then take the derivative of `arctan(sqrt(x))`.
Note: the derivative of `arctan(x)` is `1/(1+x^2)`. So, taking the derivative of `arctan(sqrt(x))` would look like `1/(sqrt(x)^2+1)`.

You then apply the chain rule and multiply `1/(sqrt(x)^2+1)` by `d/dx sqrt(x)`. You can then multiply the constant back in!

`dy/dx=23(1/(x+1))(d/dx(sqrt(x)))`