ST 552
Calculus on a Computer
Assignment 5 – The Chain
Rule
1.
Let 
and 
. What are f(g(x)) and g(f(x))?
What are their ranges and domains?
2. What are the derivatives of f and g from exercise 1 (use MAPLE)? From the chain rule, what should the derivatives of f(g(x)) and g(f(x)) be? Check.
3. A boy is flying a kite. If the kite is 60 feet above the ground, and is moving 10 ft/sec horizontally away from the boy, how fast is the string unwinding when the kite is 100 feet away (horizontally)?
4. A 1.6 meter tall woman is walking past a 3 meter lamppost. If she is walking 2 m/s directly away from the lamppost, how fast is the length of her shadow changing when she is 5 m away?
5. A lighthouse is 1 mile off shore, due west. You are on the shore, 2 miles north of the point opposite the lighthouse. The light rotates; if you see the flash every 15 seconds, how fast is the beam moving when it passes you?
6. A trough is triangular in cross section, an isosceles triangle with sides of 12 inches, and a top of 10 inches. The trough is 40 inches long. How fast is the depth changing if you are pumping one cubic foot per minute into the trough?
7.
A light is attached to a 13 inch radius bicycle tire,
at a point 8 inches from the center. If