Author Archives: hangtime

Derivatives of Trig Functions

Just the basic formulas. Without the Chain Rule, Product Rule, or Quotient rules we can't get too crazy with these things. But that's why we're looking at these now, so you can see them without the craziness that is the Chain Rule. (Can you tell I meet a lot of students who are getting crushed by the Chain Rule?)

This video appears on the page: Basic Derivative Formulas (no Chain Rule)

Difficult Power Rule Problems

The hardest power rule problems involve the chain rule, which we'll save for the Chain Rule chapter. Instead, in this video I cover a bunch of problems that look like they'd be power rule problems, except you can use algebra (FOIL, fractions, etc.) to reduce them to polynomials first. Because let's face it, your best friend in calculus is the power rule, but your second-best friend is "avoiding the quotient rule."

This video appears on the page: Basic Derivative Formulas (no Chain Rule)

Derivatives of Roots & Radicals

Again, if you need the chain rule, that's for a later chapter. However, this video covers the strategy you'll always use when you're taking the derivative of some junk under a square (or cube) root, and that strategy is this: convert it to a fraction exponent and use the power rule! The power rule is awesome.

This video appears on the page: Basic Derivative Formulas (no Chain Rule)

Derivatives of Polynomials (The Power Rule)

This is the first derivative you learn, and the easiest. Just put the old power out front, and reduce the exponent by one. But what about negative exponents? And constants? All is covered here. Just take it one term at a time, man.

This video appears on the page: Basic Derivative Formulas (no Chain Rule)

Basic Derivatives
(no Chain Rule):
Power Rule
Polynomials
Roots & Radicals
Trig Functions

This chapter covers the formulas for taking the derivatives of exponents, polynomials, powers of x, trig functions (sin, cos, tan, cot, sec, csc), exponentials, and radicals. As long as you don't need chain rule.

Part of the course(s): Basic Derivative Formulas (no Chain Rule) , ,Test Image Problem ,Calculus

Finding Equation of Tangent Line

In this video we use our refreshed knowledge of point-slope form to find the equation of the tangent line of a function at a given point. Why are we doing this? Just one of the many skills calculus is known for! Also, since derivatives are all about the slope of the curve, you can use the equation of the tangent line to approximate stuff. Pretty awesome?

This video appears on the page: Tanget Line Equations

Point-Slope Form Refresher

Most students think slope-intercept form is the bomb, but if you're in calculus, it's almost always way quicker to use point-slope form. Not sure what I'm talking about? That's why this video!

This video appears on the page: Tanget Line Equations

Tanget Line Equations
Point-Slope Form Refresher
Finding Equation of Tangent Line

A tangent line is the equation of a line that's tangent to a function at a particular point, and you find it by using derivatives. This line is important because it's slope is the "rate of change" of the function at that point. Just to make things awesome, we'll also review point-slope form of lines since that's the easiest way to find a tangent line.

Part of the course(s): ,Test Image Problem ,Calculus

Hard Limit Definition of Derivatives Problems

In this video I work some more of the same Δx problems, except with way more algebra. If you're in a lighter calc class (or pre-calc doing difference quotients), you may not see anything this hard, but if you're in AP or on your way to a science or engineering degree, buckle up, because this is just a taste of what's to come throughout calculus!

This video appears on the page: Limit Definition of Derivative

Limit Definition of Derivatives (a.k.a. Difference Quotient)

This video explains that crazy limit equation which contains all those Δx symbols, but first we learn the point of all this derivative nonsense: finding the slope of a function at each point along the curve. Sound crazy? It's the basis of calculus. These problems also show up in pre-calc as the "Difference Quotient": the math is the same, you just might have an "h" instead of Δx.

This video appears on the page: Limit Definition of Derivative

Limit Definition of Derivative
(a.k.a. Difference Quotient)
Limit Definition of Derivatives (a.k.a. Difference Quotient)
Hard Limit Definition of Derivatives Problems

These videos introduce the limit definition of derivatives, which every class covers and then forgets about. It's the one where you have to find f(x+h), then somehow plug in h and take the limit as h approaches zero.

Part of the course(s): ,Test Image Problem ,Calculus

Intermediate Value Theorem

A theorem that's in the top five of most useless things you'll learn (or not) in calculus. Unless your teacher tells you it's on the test. (And there may be a multiple choice question on the AP if you're taking that.) But even then you need to ask your teacher to get very specific about what problems you're supposed to be able to work with this thing, because it's never been obvious to me.

This video appears on the page: Intermediate Value Theorem

Intermediate Value Theorem

A theorem that's in the top five of most useless things you'll learn (or not) in calculus. Very little use, unless your teacher tells you it's on the test.

Part of the course(s): ,Test Image Problem ,Calculus

The Squeeze Theorem

These nasty puppies are limit problems with a sine or cosine which has an X in the denominator of the "argument", like sin(1/x) or cos(pi/x).

Part of the course(s): ,Test Image Problem ,Calculus

The Squeeze Theorem

These problems have a funny name, but they're pretty tricky to master. The key thing to let you know you might have one of these on your hands is if you're taking a limit of sine or cosine and two things are true: 1) there's an X in front of the sine or cosine, and 2) there's an X in the denominator of the "argument" of the trig function, like sin(1/x) or cos(pi/x).

This video appears on the page: The Squeeze Theorem ,Sine & Cosine Limits

Sine & Cosine Special Limits

This video involves a couple of annoyingly specific formulas for sine and cosine. On the down side, they'll have you asking "why would anyone ever want to know this?" On the other hand, if you see a sine or cosine in a limit problem, chances are this video will cover them!

This video appears on the page: Sine & Cosine Limits

Sine & Cosine Limits
Sine & Cosine Special Limits
The Squeeze Theorem

If a limit has a sine or cosine, this chapter covers it. Besides knowing your unit circle so you can plug in, this chapter has a couple special formulas and strategies. Also covered are special limits like sinx/x and cosx/x.

Part of the course(s): ,Test Image Problem ,Calculus

Limit Properties

This is a very specific type of problem that nobody knows what to call, but you'll most likely recognize it. They give you limits of a couple of functions, but not the functions themselves, then ask you to combine and multiply them in creative ways that only a math teacher could love.

This video appears on the page: Limit Properties

Limit Properties

You'll recognize these when you see them. They'll give you the limit of f & g (but not the equations themselves) and make you combine them. Sort of like log rules, if you're into that.

Part of the course(s): ,Test Image Problem ,Calculus

Using Limits To Find Horizontal Asymptotes

Yep, that's what we'll do. We'll also briefly review the pre-calc way of finding horizontal asymptotes of rational functions, first covered way back when in Pre-Calc.

This video appears on the page: Limits at Infinity & Asymptotes ,Inflection Points & Curve Sketching