This week we continued expanding our knowledge of derivatives. Most of the new content learned this week centered around the chain rule of derivatives. The chain rule is a formula for computing the derivative of the composition of two or more functions. This adds to our understanding of derivatives and expands our knowledge of what we can do with them. Last week we learned how to take the derivative of multiple part functions in the form of the quotient rule and the product rule. By building up an arsenal of these skills in the form of breaking larger functions into smaller pieces we are making it easier to solve problems involving derivatives. I found that this week I struggled more with this topic than in weeks previous. I believe that this is because I often have a hard time identifying when I may need to use more than just one technique to find the derivative of a function, whether it might be needing to use both the quotient and chain rule together of the product and quotient rule together.
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This week in calc we took our study of derivatives a few steps further. Starting out we learned a much less time consuming and tedious way to take the derivative of a function. You can find the derivative by multiplying the coefficient of a term in a function by its exponent and subtracting one from the exponent in each term of a function. This technique has sped up the process so much that doing more complex problems is much less intimidating. We also learned how to take anti derivatives of a function, which is just the process explained about and adding +c at the end. This lesson had made calculus as a whole much less intimidating to me as I find my rhythm in this class for the year. To end the week it felt like I was transported back to precalc as we looked at derivative rules for trig functions. I personally enjoy looking at and using trigonometric identities and today's lesson for once made a lot of sense right off the bat.
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January 2018
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