Final answer:
To solve the given expression, apply the chain rule of derivatives and break it down step by step. The solution is x = 0.
Step-by-step explanation:
To solve the expression ((d²/dx² + d/dy)(xy+2y-x²) = x), we need to apply the chain rule of derivatives. Let's break it down step by step:
- Start with the innermost derivative, which is (d/dy)(xy+2y-x²). This gives us (x + 2).
- Now, differentiate the outermost function (d²/dx²)(x + 2), where x + 2 is treated as a constant. The second derivative of a constant is always zero, so the overall derivative is zero.
- Therefore, the solution to the expression is x = 0.