implicit differentiation...?

Question

1. Consider the expression
(x^2)/9 + (y^2)/4 = 1

whose graph is an ellipse. We wish to find the slopes of the tangent lines to the graph of this ellipse at the point x = 1.

a) Solve the above expression for the variable y. How many solutions do you obtain? Graph each of these solutions separately. What do you notice when these graphs are viewed together on the same set of coordinate axes?
b) While the ellipse itself is not the graph of a function (why?), each of the solutions for y you obtained in (a) does represent a function (why?). In order to obtain an answer to our original question regarding the slopes of the tangent lines at x = 1, describe what you would do with the functions obtained in (a), and carry out this operation.

Answer 1

a) y = ±2√(1-x^2/9), two solutions

b) y = ±2√(1-1/9) = ±(4/3)√2 at x = 1
Differentiate with respect to x,
2x/9 + 2yy'/4 = 0
y' = -4x/y = ±3/√2 = ±(3/2)√2

Answer 2

merely differentiate the full factor i think of the equation your observing is; 5x^3 + x^2*y - x * y^3 = 2 Differentiate to get 15 * x^2 * dx + 2 * x * y * dx + x^2 * dy - y^3 * dx - 3 * x * y^2 * dy = 0 divide via dx and convey at the same time like words (x^2 - 3xy^2) * (dy/dx) = (y^3 -15x^2 -2xy) dy/dx = (y^3 -15x^2 -2xy)/(x^2 - 3xy^2) and your completed

Answer 3

How many times will you ask the same question?