q.5

260 III CHAPTER 3 DIFFERENTIATION RULES 3.10 Exercises 1. If V is the volume of a cube with edge length x and the cube expands as time passes, find dV/ dt in terms of dx/dt. 2. (a) If A is the area of a circle with radius r and the circle expands as time passes, find dA / dt in terms of dr/ dt. (b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1 m/s, how fast is the area of the spill increasing when the radius is 30 m? 3. If y = x3 + 2x and dx/dt = 5, find dy/ dt when x = 2. 4. If x2 + y2 = 25 and dy/dt = 6, find dx/dt when y = 4. 5. If z2 = x2 + y2, dx/dt = 2, and dy/dt = 3, find dz/dt when x = 5 and y = 12