1. So far, the functions we have been working with have been explicitly expressed in terms of one variable:
y = f(x) y = sin(x) y = 3x-5
We often see relations like these:
We can solve these for y in terms of x.
But there are some equations which we can not solve for y:
These relations are said to be implicitly defined and we can find their derivatives using implicit differentiation.
2. Examples:
3. Define orthogonal curves:
Curves which are perpendicular to each other.
Define Normal to a curve
A normal to a curve is the line perpendicular to the tangent line at that point.
Example:
