Main Ideas

$\newcommand{\arraycolsep}[3]{} \newcommand{\dd}[2][]{\frac{d #1}{d #2}} \newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}} \newcommand{\veci}{\vec{\hat{\bf\imath}}} \newcommand{\vecj}{\vec{\hat{\bf\jmath}}} \newcommand{\utan}{\vec{\hat{t}}} \newcommand{\unormal}{\vec{\hat{n}}} \newenvironment{amatrix}[1]{% \begin{bmatrix} }{% \end{bmatrix} }$

$\newenvironment {prompt}{}{} \newcommand {\ungraded }[0]{} \newcommand {\HyperFirstAtBeginDocument }[0]{\AtBeginDocument }$

Here are the main points that are addressed in the video. Please read these and think about them as you watch.

Implicit differentiation is a procedure which can be used as long as y is locally a function of x.
If we treat $y$ as a function of $x$ locally, we can use the chain rule to take the derivative of both sides of an equation with respect to $x$ .
For example, if we see a $y^2$ in an equation, the derivative with respect to $x$ would be $2 y y'$ , due to the chain rule.