Test 2: Concept Review

• Special derivatives (e.g. derivatives of a constant, f(x)=x).
• Special limits (e.g. ).
• Differentiation Rules: Sum, difference, product, quotient, constant multiple, power.
• The Chain rule: how to use it; how to represent it. ``The derivative of f of stuff is equal to f prime of stuff times stuff prime.'' Remember that this is a very mechanical process: identify the composition, find the two derivatives, and apply the rule!
• Applications of the derivative (e.g. biology, physics, chemistry, economics) as an instantaneous rate of change.
• Derivatives of trig functions (especially sine and cosine); definition of the other trig functions (e.g. secant); how to derive the derivatives of the other trig functions from those two principal trig function (quotient rule!).
• Implicit differentiation; graphs of objects (e.g. circles) more general than functions; orthogonal families and their meaning.
• Related rates (drawing a good picture, establishing well-named variables and constants, finding the data, finding an equation relating the variables, and using implicit differentiation).
• Higher derivatives; physical meaning of the higher derivatives (e.g. velocity, acceleration, jerk).
• Tangent line approximation; differentials; differentials versus increments; error of approximation and relative error.

In the meantime, don't forget the basics from the first test: how to find domains of functions, the definition of derivatives as limits, etc. While the focus will be on the new material, you will still be expected to be able to use the old stuff!