# Derivatives and Implicit Differentiation

Published on: Thu Mar 11 2010

How do you find two tangent lines passing through a point? The point is not a point on the line! So decide on an arbitrary point on the line and call it f(a). Then solve for the slope m in terms of a (Find f’(a)). Then plug in your values and solve for the tangent line at the two points. Derivative Example Problems Rule: Apply log rules when you see logs!!!!!! (You want to expand as much as possible) Implicit Differentiation We briefly started to talk about implicit differentiation. So a function is y=f(x). or “y as described by function f with respect to point x equals”. And this seems to be the key here. So we started using this new notation for derivatives, instead of the usual f prime. To start, look at a very easy example, x2. y equals x2 which is the same as, f(x) equals x2, which says that y = f(x).” “The derivative of the function which equals y with respect to point x equals f prime, which is equivalent to the derivative of x2 equal 2x.”