In a calculus assignment, I was asked to find the derivative of the following:
$$yx^4=\frac{2}{3}$$
Solving for y then differentiating produces:
$$\frac{\partial y}{\partial x}=\frac{-8}{3x^5}$$
The material lists this as the correct answer. However, the two computer algebra systems I've entered this into use implicit differentiation and produce the following solution:
$$\frac{\partial y}{\partial x}=\frac{-4y}{x}$$
Which solution is correct and when should one use implicit differentiation instead of solving for y?