Implicit Differentiation

Implicit Differentiation is a technique that we use when we are taking the derivatives of functions with other variables inside of them that are also functions of that variable.

For example, if we are differentiating with respect to x, a function y, in terms of x, where this function itself has an y inside, we treat that y as a function of x and its derivative accordingly.

Try a very simple example:

Now, let's get a bit more complicated:

A message:

Don't worry if all of these concepts seem "jumpy" for now, or may not "make sense" totally, but we'll have some "consolidation" chapters later where we see how all of them connect.

Let's go into using implicit differentiation to determine Derivatives of Trigonometric Inverse Functions