If xʸ · yˣ = 1, then dy/dx at (1, 1) is:

If xʸ · yˣ = 1, then dy/dx at (1, 1) is:

• A. −1
• B. 1
• C. 0
• D. 2

Answer: A) −1

Explanation: y log x + x log y = 0. Differentiate: y′ log x + y/x + log y + (x/y) y′ = 0. At (1,1): log 1=0, so y/1 + 0 + 0 + (1/1) y′ = 0 → 1 + y′ = 0 → y′ = −1.