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Derivatives


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  1. At the top and bottom of a curve (Max and Min), the slope is zero. The second derivative shows whether the curve is bending down or up. Here is a real-world example of a minimum problem: What route from home to work takes the shortest time?

  2. Calculus-Derivative: Finding the slope (or derivative) of a curve at a particular point.

  3. Using derivatives to solve rate-of-change problems.

  4. Approximating a function with a polynomial by making the derivatives equal at f(0) (Maclauren Series).

  5. Chain rule using partial derivatives (not a proof; more intuition).

  6. Doing both proofs in the same video to clarify any misconceptions that the original proof was "circular".

  7. Why the quotient rule is the same thing as the product rule. Introduction to the derivative of e^x, ln x, sin x, cos x, and tan x.

  8. More intuition of what a derivative is. Using the derivative to find the slope at any point along f(x)=x^2.