is used to encode infinitesimal changes
used to act as a placegolder value
divide wrt time to get rate of change CHAIN RULE
Chain Rule with More Variables
Let when then,
(tangent to the level surface at any given point):
Direction of is the direction of fastest increase of
) where are not independent and .: minima/maximize a multi-variable function (
These can be obtained on combining the given restraints with the following.
where the level curves of and are tangent to each other ().: to find
: Take care that the point is indeed a maxima or minima as required and not just a saddle point (second derivative test won't be applicable so be vigilant).