This week in AP Calculus we dove into derivatives with composite functions. First, we did a little lab that explored the derivative of sin functions when the inside was changed from x to something else like 3x. From this, we got an introduction to the chain rule that states (f o g)' = (f' o g) * g'. While this rule looks neat compared to some other rules we learned, such as the quotient rule and product rule, it definitely can become just as messy. When working with derivatives in general, I tend to get lost and make mistakes as the problem gets messier and messier, so when I am tasked with finding the derivatives of composite functions that contain more than just two functions, and things such as square roots or fractions, I start getting the solution wrong.
If I had to rate my understanding and ability to use these new rules all together, on a scale of 5, I'd probably rate myself around a 3. I feel that I have a decent understanding of derivatives and tangent lines now after all we've done, but even with this I tend to make silly mistakes all the time, or start working in circles when finding a complicated derivative. This goes for the "Critical Thinking" problems that require you to think a little outside of the box to get the solution, because for these problems I tend to just go off on a completely irrelevant direction for awhile before discovering that I've been doing it all wrong. I'm looking to hammer down all these concepts before the next test, and I'm also hoping that the test won't be too difficult.
If I had to rate my understanding and ability to use these new rules all together, on a scale of 5, I'd probably rate myself around a 3. I feel that I have a decent understanding of derivatives and tangent lines now after all we've done, but even with this I tend to make silly mistakes all the time, or start working in circles when finding a complicated derivative. This goes for the "Critical Thinking" problems that require you to think a little outside of the box to get the solution, because for these problems I tend to just go off on a completely irrelevant direction for awhile before discovering that I've been doing it all wrong. I'm looking to hammer down all these concepts before the next test, and I'm also hoping that the test won't be too difficult.