2. Simplifying 2 nd Derivatives with Substitutions Find in terms of x and y for Make a substitution Look for one last substitution Look familiar?
3. That was intense! Often we are not interested in the simplest form of the derivative, but in calculating a number from that form, so we can substitute in x and y after taking derivative, even without other simplification, and be okay. Find equations for the normal line to the circle at the given point. at point (3, 4). [A normal line is perpendicular to the tangent line at the point.] In modified point slope form, Simplify and you get or
4. Implicit Differentiation things to watch out for: Identifying when to use product rule! Identifying when to use chain rule ! Identifying constants as coefficients or as terms! Product rule, coefficient Chain rule Constant
