implicit diffirentation
posted by pav .
y4 + xy = x3 – x + 84
(a) Find dy/dx at the two points on the graph with xcoordinate 0.
Hint: Set x=0 in the equation and solve for y to find the two points.

Do you mean
y^4 + xy = x^3  x + 84 ??
if so, then
4y^3 dy/dx + x dy/dx + y = 3x^2  1
dy/dx(4y^3 + x) = 3x^2  1  y
dy/dx = (3x^2  1  y)/(4y^3 + x)
now follow the hint