SEAMIC_Functions: Derivatives III

In this video the rule of quotient, product, and chain rule are explained with examples. The instructor emphasizes that when calculating the derivative of a quotient, one should not simply calculate the derivative of the numerator and denominator separately. Instead, the correct rule is applied to find the derivative. Additionally, the chain rule is discussed, which involves finding the derivative of an external function at an internal function. The video provides several examples, including finding the derivative of a polynomial and a composition of functions involving logarithm, cosine, and quotient. Finally, the instructor reviews important theorems, such as the relationship between the derivative and the increasing/decreasing nature of a function, and the connection between the second derivative and convexity/concavity of a function.