ImplicitDifferentiation
LearningObjectives
A studentwill be able to:
- Find the derivativeof varietyof functionsby usingthe techniqueof implicitdifferentiation.
Considerthe equation
We wantto obtainthe derivativedy/dx. One way to do it is to first solvefory,
and then projectthe derivativeon both sides,
Thereis anotherway of findingdy/dx. We can directlydifferentiateboth sides:
Usingthe ProductRule on the left-handside,
Solvingfordy/dx,
But since , substitutiongives