If you're reading this, chances are you already know what the Chain Rule is and are ready to dive in. I'll just take this moment to encourage you to work the problems in the videos below along with me, or even before you see how I do them, because the Chain Rule is definitely something where actually DOING it is the only way to get better. With the harder problems you get into chain rules within chain rules within chain rules, so the only way to figure out which way is up is to practice getting through them. More than with any other topic practically. Good luck!
What Is The Chain Rule? (free)
I'm not going to throw you any major calculus theory about where the chain rule comes from. That will just confuse you, and besides, I don't really know where this thing comes from. Instead, in this video I'll show you how to spot whether a problem needs the chain rule or not, because that's the crucial first step in any derivative problem. In later videos we'll get into how to actually use the chain rule in each problem type.
The Power Rule (with Chain Rule)
In a previous derivatives chapter we already saw how to use the power rule to take derivatives of powers of x. Now we'll use the chain rule to take derivatives of anything -- polynomials, sine, cosine -- to a power, with the help of u'.
Derivatives of Roots & Radicals (with Chain Rule)
In a previous derivatives chapter we saw how to take derivatives of square roots and cube roots of x. Now, thanks to the chain rule, we'll take derivatives of all kinds of crazy roots and radicals.
Derivatives of Trig Functions (with Chain Rule)
We already saw how to differentiate trig functions as long as they only had an X or theta. Now we'll see how differentiate harder stuff like sin(3x), tan(x^{2}+4), or even sec(e^{x}).
Derivatives of Exponentials (with Chain Rule)
Without the chain rule, it's pretty boring differentiating e^{x} all the time, because it's always the same. But thanks the chain rule, your teacher will now demand that you take the derivatives of e with all kinds of crazy exponents, and it will be up to you to deliver.
Derivatives of Natural Logs (with Chain Rule)
Most Calculus teachers don't emphasize derivatives of natural logs. However, these gems are very common later in the semester when you're doing integrals, so I figure we might as well take a look at them now. Plus, they're a great way to practice the chain rule!
Hard Chain Rule Problems
These are just a bunch of really hard chain rule problems, where we'll have to use the chain rule two or three times on the same problem. These will help get you used to the most confusing aspect of the chain rule, which is figuring out when you're done once you're in two or three chain rules deep.
Derivatives of Inverse Trig Functions
In this video I show you how to use the inverse trig function derivative formulas. Most classes don't do these, but if you do, you're in luck! Also, I try and show you how you can use any of the more obscure trig derivative formulas that you probably have kicking around the appendix of your book.
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