Section Summary: 3.6

  1. Definitions

    None!

  2. Theorems

  3. Properties/Tricks/Hints/Etc.

    Hmmmm....

  4. Summary

    The chain rule is the secret to differentiating compositions of functions, and this is a terribly important rule which you must memorize and understand.

    The hardest thing about the chain rule is probably identifying the composition of functions. Given an expression, e.g. tex2html_wrap_inline137 , you need to realize that tex2html_wrap_inline139 , and g(x)=2x-1 (then apply the rule correctly, of course:

    displaymath112

    Sometimes we talk about ``outer function'' and ``inner function''. The inner function is the first function x meets on its transformation. The inner function returns a value u, which serves as the input to the outer function which returns a value y. The composite function of inner and outer thus takes a value x and returns a value y.

Problems we might consider: 2-10 even; 55, 58, 66, 67; at seats: identify f and g in 7-41 odd; on the board: 1, 5, 36, 57


LONG ANDREW E
Fri Feb 14 10:33:08 EST 2003