Strategies in solving problems:
1.
Read the problem carefully.
2.
Draw a diagram or pictures.
3.
Introduce notation. Assign symbols to all quantities as functions of time.
4.
Express the given information and required rate in terms of derivatives.
5.
Write an equation relating the various quantities.
6.
Use geometry to eliminate one variable by substitution, if possible.
7.
Use Chain Rule to differentiate both sides with respect to time.
8.
Substitute and solve for unknown rates.

A ladder 10 feet long is resting against the wall. If the bottom of the ladder slides away at the rate of 1 ft/s, how fast is the top of the ladder sliding down when the bottom is 6 ft from the wall?

At noon, ship A is 150 km west of ship
B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4PM?

A spotlight on the ground shines on a wall 12 meters away. If a man 2 meters tall walks from the spotlight toward the building at a speed of 1.6 m/s, how fast is the length of his shadow on the building decreasing when he is 4 meters from the building?

Water is leaking out of an inverted, conical tank at a rate of 10,000 cubic cm/min at the same time that water is being pumped into the tank at a constant rate. The tank has height of 6 meters and diameter at the top is 4 meters. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 meters, find the rate at which water is being pumped into the tank.

A lighthouse is located on a small island 3 km away from the nearest point P on a straight shoreline and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is
1 km from P?