We discuss how we will tackle the next phase of calculus; the derivative!

We consider the derivative from an analytic point of view; digging into the algebraic notation and manipulation for instantaneous rates of change.

We consider the derivative from an analytic point of view; digging into the algebraic notation and manipulation for instantaneous rates of change.

We discuss and justify computing derivatives with variable input and introduce the idea of derivatives as functions.

We discuss how continuity and differentiability are interrelated.

We develop the rules needed to split functions across addition and subtraction signs, which allows us to take derivatives term by term.

We develop the power rule, otherwise known as the polynomial rule, to take derivatives of terms with the form $x^n$ for any real value $n$.

We develop the technique for decomposing the product of functions for derivatives, introducing the “Product Rule”.

We introduce the quotient rule as a way to decompose a quotient of functions when taking a derivative.

We discuss and ultimately develop a rule that allows us to take derivatives of compositions of functions. The so-called Chain Rule.

We discuss how to tackle the problem of applying chain rules when you have functions with several layers of composition.

We discuss how to take a derivative of an implicitly defined function.

We develop the rules to differentiate exponential functions.

We develop the rules needed to differentiate logarithmic functions.

We discuss a new differentiation technique, useful for functions with large number of products - Logarithmic Differentiation.