Implicit Differentiation
What The Heck Is Implicit Differentiation?
Glad you asked so politely. This is where you have an equation like xy-y=3 and they want you to find dy/dx, a.k.a. y' (y prime). Previously, we've only taken derivatives of functions with just one y or f(x); adding that second y makes these a whole new can of worms! These aren't too bad, you just have to be careful to NEVER forget y'.
Finding Tangent Lines Using Implicit Differentiation
We covered tangent lines pretty well in the finding tangent lines chapter, but in this video we'll be using implicit differentiation to find the derivative (a.k.a. slope) of the tangent line. Then it's just plug-and-chug using point-slope form!
Finding Second Derivatives With Implicit Differentiation
The derivative of the derivative is the "second derivative", also known as d2y/dx2 or y'' (y double prime). Finding the second derivative is as easy as just taking the derivative of the first derivative, but in these implicit problems you end up having to keep plugging in stuff at each step if you want full credit. You'll see what I mean.