Grade 12 Calculus and Vectors
Chapter 2: Derivatives

Derivative is the instantaneous rate of change and sometimes referred to as the rate of change (i.e. how fast or quickly is something changing). This chapter will look at the concept of derivative, and the procedure for finding derivatives of functions. The process of finding derivative is called differentiation, and we will start by differentiating polynomials and rational functions using sum, difference, product, quotient, power and chain rules as well as, composite function differentiation rule. It is highly recommended that students take the time to master these techniques because this is the very foundation from which all Calculus topics will build upon.

HINT: It is evident from the chapter and overall course reviews that slope = m = rise/run = ΔY / ΔX = rate of change = tangent = limits = gradient. Now, to add a new word to the list: yes, you’ve guessed it- its “DERIVATIVE!” Derivative is similar to all of the previously mentioned terms, but it’s more synonymous to instantaneous rate of change.

2.1 Introduction to Derivatives (limit of f(x) as h—>0)



2.2 Derivatives: Power Rule



2.3 Derivatives: Sum and Difference Rules



2.4 Derivatives: Product Rule



2.5 Derivatives: Quotient Rule



2.6 Derivatives: Chain Rule [Composite functions]



2.7 Derivatives: Power Rule for Composite Functions