y4 + xy = x3 – x + 84

Question

(a) Find dy/dx at the two points on the graph with x-coordinate 0.
Hint: Set x=0 in the equation and solve for y to find the two points.

Answer 1

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