For the implicit function x³ + y³ = 3axy, what is dy/dx?
For the implicit function x³ + y³ = 3axy, what is dy/dx?
- A. (ay − x²) / (y² − ax)
- B. (ax − y²) / (y² − ax)
- C. (x² − ay) / (y² − ax)
- D. a / (x² + y²)
Answer: A) (ay − x²) / (y² − ax)
Explanation: Differentiate both sides: 3x² + 3y²y' = 3a(y + xy'). Rearrange: y'(y² − ax) = ay − x², yielding dy/dx = (ay − x²) / (y² − ax).
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