Calculus IV: The Chain Rule
February 14th, 2007 by SplineGuy
In class on Tuesday, we stated and used the chain rule for partial derivative:
For 
be a function of 
variables, such that 
is a function of 
variables for each 
then
for each 
We derived the result called the Implicit Differentiation theorem which gives you a shortcut to perform (single-variable) implicit differentiation using partial derivatives.
We just got started talking about directional derivatives. Next time will define the gradient and begin to show some simple useful results involving it. Then, we’ll be able to begin studying optimization of functions of several variables.
46lgdk3lshr056rr