Math 205 Lecture 11 - Implicit Differentiation

Welcome to lecture 11 of Math 205 - Elements of Calculus.

In this lecture, though off to a bit of a hiccup of a start, we get into implicit differentiation. That is, differentiating expressions where our dependent variable is not explicitly defined, but rather mixed up with the independent variable in some mathematical expression, such as x^2 + y^7 - 2xy = 3. We learn how to find dy/dx in such an expression, without explicitly solving for y first. This is important, since many relationships arise in nature where our independent and dependent variables are mixed up like this. Implicit differentiation also helps us to derive many important formulas and is useful for applications such as related rates.

We go over the basics in this lecture and will pick up with more on implicit differentiation and log differentiation next time--as well as, perhaps, linear approximation and marginal analysis.