Question

What is the derivative of `arctan (x/2)`?

Answer 1

`(dy)/(dx)=1/2cos^2(arctan(x/2))`

Explanation:

As `y=arctan(x/2)`

`tany=x/2`

Hence, `sec^2yxx(dy)/(dx)=1/2` or

`(dy)/(dx)=1/2cos^2y=1/2cos^2(arctan(x/2))`