📝 DIFFERENTIATING EQUATIONS TO RELATE RATES

Q1. If \(x\) and \(y\) are functions of \(t\) related by \(y = x^2\), and \(\frac{dx}{dt} = 3\) when \(x = 2\), find \(\frac{dy}{dt}\).

💡 Difficulty: easy | ✅ Correct: C

Q2. If \(x\) and \(y\) are functions of \(t\) related by \(x^2 + y^2 = 25\), and \(\frac{dx}{dt} = 4\) when \(x = 3, y = 4\), find \(\frac{dy}{dt}\).

💡 Difficulty: medium | ✅ Correct: D

Q3. A ladder 10 ft long leans against a wall. If the bottom is pulled away at 2 ft/s, how fast is the top sliding down when the bottom is 6 ft from the wall?

💡 Difficulty: hard | ✅ Correct: A