All of the cases that we've looked at so far have involved functions that were all functions of $x$, i.e. they all look like $y=f(x)$ where the $f(x)$ part only has *x*'s in it. There are a lot of functions that can be written that way but there are also a lot of functions that can't, e.g. the equation of a circle, $x^2 + y^2 = 1$. We can still differentiate these functions if we recognize that $y$ is a function of $x$ even if it can't be explicitly written that way. The process for doing this is called "implicit differentiation".

# Video Lectures

Sometimes, you have a formula that describes a relation (not necessarily a function any more) and you can't solve it for y. The function is still changing so it still has a rate of change. Implicit differentiation is a technique that will let us find it.