Solve the given equation for `y`: `y=+-3sqrt(1-x^2/4)`. The positive solution corresponds to the top half of the ellipse.
`(dy)/(dx)=3*1/2*1/sqrt(1-x^2/4)*d/(dx)(1-x^2/4)=3/2*1/sqrt(1-x^2/4)*(-2x)/4=- 3/4*x/sqrt(1-x^2/4)`.
At `x=1`, `(dy)/(dx)=-3/4*1/sqrt(3/4)=-sqrt(3/4)=-sqrt(3)/2.`