Final answer:
To find d²y/dx² or the second derivative for an implicitly defined function, explicit differentiation must be performed twice in a row. The question doesn't provide the necessary specific function to derive the second derivative, making it impossible to choose the correct answer from the options.
Step-by-step explanation:
To find d²y/dx² for an implicitly defined function, you would need to perform implicit differentiation. Unfortunately, the information provided in the question is insufficient to determine the correct answer from the options listed (a) through (d). To solve such a problem, you would typically differentiate both sides of the equation defining y implicitly with respect to x, solve for dy/dx, and then differentiate again to find d²y/dx².
However, if this question relates to a specific implicit equation which we denote as F(x, y) = 0, then we need that exact equation to find its second derivative. An example process without the specific function would be:
- Differentiate both sides of F(x, y) with respect to x using the chain rule, which will give us dy/dx in terms of x and y.
- Differentiate the resulting equation again with respect to x to find the second derivative, d²y/dx², also in terms of x and y.