Find the derivative dy/dx of the implicit function x^2 + 2xy + y^3 = 4 at the point (1, 1).
Answer and explanation
Correct answer: B. -4/5
- Step 1: Differentiate both sides with respect to x: 2x + 2(y + x dy/dx) + 3y^2 dy/dx = 0. Step 2. Collect dy/dx terms: dy/dx (2x + 3y^2) = -(2x + 2y). Step 3. Substitute (x = 1, y = 1): dy/dx (2(1) + 3(1)^2) = -(2(1) + 2(1)) => dy/dx 5 = -4 => dy/dx = -4/5. Answer: -4/5. Why not the others:* -2/3 forgets the product rule on 2xy; +4/5 reverses the sign.
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