Use implicit differentiation to find y' and y" :
#1. x2 + y2 = 1
#2. x2/3 + y2/3
#3. y2 = x2 + 2x
#4. y2 + 2y = 2x + 1
Related Rates:
#1 Gas is escaping from a spherical balloon at a rate of 10ft/hr3. At what rate is the radius changing when the volume is 400ft3?
#2 As a circular griddle is being heated, its diameter changes at a rate of 0.01cm/ min . When the diameter is 30cm, at what rate is the area of the griddle changing?
#3 A ladder 20 ft long leans against a vertical building. If the bottom of the ladder slides away from the building horizontally at a rate of 2 ft/sec, how fast is the ladder sliding down the side of the building when the top of the ladder is 12 ft above the ground?
#4 A man on a dock is pulling in a boat by means of a rope attached to the bow of the boat lit above the water level and passing through a simple pulley located on a dock 8fi above the water level. If he pulls in the rope at a rate of 2fi/sec, how fast is the boat approaching the dock when the bow of the boat is 24fi from the point that is directly below the pulley?
#5 A girl starts at point A and runs east at 10 fi /sec. One minute later, another girl starts at point A and runs north at 8ft/sec. At what rate is the distance between the girls changing one minute after the second girl starts?
#6 A water tank has a shape of an inverted right circular cone (those white drink cups on the side of a water cooler) of altitude 12 ft and base radius of 6ft. If water is pumped into the tank at a rate of 10 gal/min , approximate the rate at which the water level is rising when it is 3ft deep.
Use logarithmic differrentiation to solve the following and vefiy your answer by a diffrent technique:
#1. y = √x(x+1)
#2. y = √(x + 3)sinx