Final answer:
The question involves finding the derivative y' of a function by using implicit differentiation and potentially applying the chain rule.
Step-by-step explanation:
The student is asking how to find the derivative, denoted as y', of the function given by the fourth root of (y+3)^3 equated to −1+x. To find y', we would employ implicit differentiation since the equation involves both x and y.
To perform implicit differentiation, we take the derivative of both sides with respect to x, applying the chain rule for the left side. After differentiating, we solve for y' to get the explicit expression for the derivative in terms of x (and potentially y if the equation does not allow for an explicit solution for y).