Put `u = x^2+ 0.5`.

Then we have: `y = 3\ cos^-1 u`

`y=3\ cos^-1(x^2+0.5)`

`(dy)/(dx) =3[(-1)/(sqrt(1-u^2))(du)/(dx)]`

`=3[(-1)/(sqrt(1-(x^2+0.5)^2))(d(x^2+0.5))/(dx)]`

`=3[(-1)/(sqrt(1-(x^2+0.5)^2))(2x)]`

`=(-6x)/(sqrt(1-(x^2+0.5)^2)`

Expanding and simplifying gives:

`(dy)/(dx)=(-6x)/(sqrt(0.75-x^4-x^2)`

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