Use implicit differentiation to find y' and y" :

#1. x² + y² = 1

#2. x^2/3 + y^2/3

#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