You can take the derivatives of f(x) and g(x), but what about f(g(x)) or g(f(x))? The chain rule gives us this ability. Because most complex and hairy functions can be thought of the composition of several simpler ones (ones that you can find derivatives of), you'll be able to take the derivative of almost any function after this tutorial. Just imagine.

Discover what magic we can derive when we take a derivative, which is the slope of the tangent line at any point on a curve.

The topic that is now known as "calculus" was really called "the calculus of differentials" when first devised by Newton (and Leibniz) roughly four hundred years ago. To Newton, differentials were infinitely small "changes" in numbers that previous mathematics didn't know what to do with. Think this has no relevence to you? Well how would you figure out how fast something is going *right* at this moment (you'd have to figure out the very, very small change in distance over an infinitely small change in time)? This tutorial gives a gentle introduction to the world of Newton and Leibniz.

We told you about the derivatives of many functions, but you might want proof that what we told you is actually true. That's what this tutorial tries to do!

This 18-minute video lesson shows how to Approximate a function with a Taylor Polynomial.

This 6-minute video lesson looks at the Taylor Series at 0 (Maclaurin) for e to the x.

This 9-minute video lecture is part 4 of derivatives: introduction to the chain rule.

This 8-minute video lesson continues to cover the Calculus-Derivative: Finding the derivative of y=x^2.

This 8-minute video lesson looks at how to use a triple integral to find the mass of a volume of variable density.

This 12-minute video lesson demonstrates how to figure out the boundaries of integration.

This tutorial classifies regions in three dimensions. Comes in useful for some types of double integrals and we use these ideas to prove the divergence theorem.

U-substitution is a must-have tool for any integrating arsenal (tools aren't normally put in arsenals, but that sounds better than toolkit). It is essentially the reverise chain rule. U-substitution is very useful for any integral where an expression is of the form g(f(x))f'(x)(and a few other cases). Over time, you'll be able to do these in your head without necessarily even explicitly substituting. Why the letter "u"? Well, it could have been anything, but this is the convention. I guess why not the letter "u" :)