Question

How do you find dy/dx by implicit differentiation?

x^3 + y^5 = 1

Answer 1

3 x^2 dx + 5 y^4 dy = 0

dy/dx = -3 x^2/5y^4

if needed as function of x only then
y = (1-x^3)^.2
y^4 = (1-x^3)^.8
so
dy/dx = -(3/5)x^2/(1-x^3)^.8