RES.18-005 | Spring 2010 | Undergraduate

Highlights of Calculus

Derivatives (12 videos)

Chains f(g(x)) and the Chain Rule

A chain of functions starts with y = g(x)   Then it finds z = f(y).  So z = f(g(x))
Very many functions are built this way, g inside f .   So we need their slopes.

The Chain Rule says :  MULTIPLY THE SLOPES  of  f and g.

Find dy/dx for g(x).   Then find dz/dy for f(y). 
Since dz/dy is found in terms of y, substitute g(x) in place of y !!!
The way to remember the slope of the chain is dz/dx = dz/dy times dy/dx. 
Remove y to get a  function of x !   The slope of z = sin (3x) is 3 cos (3x).

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

Subtitles are provided through the generous assistance of Jimmy Ren.

Course Info

As Taught In
Spring 2010
Learning Resource Types
Lecture Videos
Lecture Notes