Question

How to find the derivative of `3arccos(x/2)`?

Answer 1

-`3/[2sqrt(1-x^2/4)]`

Let y= 3 arc cos`x/2`, so that `y/3` = arc cos`x/2`
Thus, cos`y/3`= `x/2` and hence sin`y/3` = `sqrt(1- x^2/4)`
Now differentiate, -`1/3` sin`y/3` `dy/dx` = `1/2`

`dy/dx`= -`3/[2sin(y/3)]`

= -`3/[2sqrt(1-x^2/4)]`