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C.4 Chain Rule – Used to Find Yet More Derivatives

On this screen, we’re going to use the Chain Rule to find yet more derivatives. This will both (1) give you even more crucial practice at using the Chain Rule, and (2) will let you find the derivative of things like $2^x,$ $\sec x,$ $\cot x,$ and so forth.

Let’s see first how we can easily extend our new knowledge that $\dfrac{d}{dx}e^u = e^u \dfrac{du}{dx}$ to find the derivative of $a^x,$ now much more easily than we could before we had the Chain Rule as a tool.

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Let’s next use the Chain Rule as an alternate way to develop the Quotient Rule, starting from the Product Rule.

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And let’s find some more common trig derivatives.

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The next problem develops a slick insight into the derivatives of even and odd functions.

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This screen concludes our focus on the Chain Rule, though of course we’ll be using it often as we proceed.

For now, what are your thoughts about using this crucial rule? What advice would you give to someone just starting to learn what it’s about and how to use it? What remaining questions do you have? Please post on the Forum and let the Community know!