How to find the slope of f(x) times g(x) ?   Use the Product Rule.

The slope of  f(x)g(x)  has two terms:

       f(x) times (slope of g(x))   PLUS  g(x) times (slope of f(x))

The Quotient Rule gives the slope of f(x) / g(x) .   That slope is 

    [[  g(x) times (slope of f(x))  MINUS  f(x) times (slope of g(x)) ]] / g squared

These rules plus the CHAIN RULE will take you a long way.

Professor Strang’s Calculus textbook (1st edition, 1991) is freely available here.

Subtitles are provided through the generous assistance of Jimmy Ren.