This applet looks at the chain rule in the case when a parameterized
curve from R
is composed with a function from R2
to R to
produce a function
from R to R.
The standard situation starts with a curve in
x-y plane parameterized by t, then considers z as a function of x and
y. In the composition we then consider z a as a function of t.
In understanding this version of the chain rule we want to introduce a
second parameter, s, so that we think of x as a function of s and y as
a function of t. The parameterized curve corresponds to the
diagonal line in the s-t plane
You may find it useful to review the chain rule for functions of one variable
The formula for the chain rule is