From Average to Instantaneous: Rates of Change
Alright, let's kick off Unit 2 by tackling the fundamental idea of rates of change. Now, average rat
Defining the Derivative: Our New Best Friend
Alright, so we've established that the instantaneous rate of change is the slope of the tangent line
Estimating Derivatives: When You Don't Have a Formula
Okay, so far we've talked about finding the *exact* derivative using limits. But what if you don't h
Differentiability and Continuity: When Derivatives Don't Exist
Alright, so we know what a derivative is: the slope of the tangent line. But is a function *always*
The Power Rule: Our First Derivative Shortcut!
Okay, are you ready for some magic? Because doing limits *every single time* we want a derivative? N
Derivative Rules for Sums, Differences, Constant Multiples, and Products
Okay, the Power Rule is awesome, but what if you have more complex functions? We're building our dif
Derivative Rules for Quotients: The Low D-High Rule!
Alright, we've got products, now what about fractions? Enter the **Quotient Rule**! This one is a bi
Derivatives of Sine and Cosine: Trig's Entrance!
And finally, for this unit, we need to bring in our trigonometric friends: sine and cosine! You abso