# 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, x^{2}.
“*y* equals *x*^{2} which is the same as, *f(x)* equals *x*^{2}, 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 *x*^{2} equal *2x*.”