We have reached the world of Derivatives. This is a very powerful unit where we will be exploring some very abstract concepts. Most students struggle over the algebra (rather than the calculus components) so it is essential that we brush up on our algebra skills. Namely:
- Simple Composition Functions
- Solving Equations (using the quadratic formula)
- Rates of Change
- Simplifying Rational Functions that include addition and subtraction.
In class we have (or have already) talked about derivatives and what they mean. I believe this video is a nice summary of the theory discussed in class. He speaks quickly but repeats ideas many times.
We have talked about “shortcuts” for doing derivatives in class, but these are more just techniques for doing the long derivatives. We have discussed a lot of the theory in class. If you want more theory, check out this video to understand visually the theory behind the derivative.
Derivative Rules Explained (video sets from Khan Academy)
- Power Rule – https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-5/v/power-rule
- Constant, Sum, Difference and Constant Multiple Rule – https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-6a/v/derivative-properties-and-polynomial-derivatives
- Connected with Power Rule – https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-6b/v/differentiating-polynomials-example
- Product Rule – https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-8/v/applying-the-product-rule-for-derivatives
- Quotient Rule – https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-9/v/quotient-rule