Professor Dave here, let’s get back to graphing. I’m sure you got enough of graphing when we learned algebra, but we need to expand our abilities now that we understand differentiation. First, as we recall, the derivative of a function at a particular point is equal to the rate of change in the function at…

# Tag: professor dave

## Continuous, Discontinuous, and Piecewise Functions

It’s Professor Dave, let’s learn about continuity in functions. We’ve just learned about a variety of functions, and up until now, they have all been continuous functions. These are functions where there are no gaps whatsoever. Any X value can act as an input, and we get all the corresponding values for the function as…

## Protein Structure

Hey guys, it’s Professor Dave, I want to tell you about proteins. So we know about amino acids, and these are the monomers that will form proteins, which are also known as polypeptides. Proteins are polymers of amino acids, and they are the most diverse type of biomolecule in your body. Different kinds of proteins…

## Derivatives of Composite Functions: The Chain Rule

Professor Dave here, let’s learn the chain rule. We know how to take derivatives of polynomials in standard form, trigonometric functions, as well as simple products and quotients of these functions. But unfortunately, functions can get more complicated than this. What if we have a trinomial raised to an exponent? Or a trig function operating…

## Graphing Rational Functions and Their Asymptotes

74) Graphing Rational Functions and Their Asymptotes Professor Dave again, let’s learn about asymptotes. We just learned how to graph higher degree polynomials, but we also need to graph rational functions. These are functions that are expressed as quotients of polynomial functions. This can make things a bit trickier for a number of reasons. First,…

## Graphing Trigonometric Functions

Professor Dave here, let’s graph some trig functions. We’ve just spent some time learning about the six trigonometric functions, as well as how they relate to one another, and the unit circle. Just like any other function, we will want to be able to graph them, but there are some interesting things that we can…

## Hyperbolic Functions: Definitions, Identities, Derivatives, and Inverses

Hey it’s Professor Dave, let’s learn about hyperbolic functions. We’ve learned enough math up to this point that many of the mysterious buttons on a sophisticated calculator have been elucidated. There are trig functions, inverse trig functions, logarithms, exponential functions, and lots of other things that are now well understood. But on certain calculators you…

## Trigonometric Functions: Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent

Professor Dave here, let’s learn the trigonometric functions. In the last clip, we introduced radians, and drew some circles. But trigonometry is about triangles, so where do those come in? Well let’s go to our coordinate plane and draw a circle. Now let’s draw a radius and start to move it through quadrant one. Wherever…