Blog Post 6: Derivatives, but wait... there's more?

1. Derivatives do not exist:

1. f(x)=|x| 
2. cusp
3. jump
4. asymptote

(anywhere with a corner or where the limit does not exist)

2. Implicit differentiation:

Take a derivative of a function with regards to a variable that may not be in the function or is not the only variable in the function. Every time you find the derivative of a piece, you multiply by the derivative of the variable over the derivative of the variable you are finding the derivative with regards to. Example: 

3. The most important thing to remember in a related rate problem is to always multiply by the correct d(variable)/dt so that you can correctly plug in given information to find the correct answer.