At the beginning of this week, I had some struggles. We did a worksheet on more chain rule problems, and even though I didn't have any problems with the chain rule, for some reason I was having a lot of problems. First of all I kept taking the chain rule over and over. When I was supposed to just multiply by the derivative of the inside, I starting multiplying the answer by the second derivative. It was a mess and I ended up doing significantly more math than was necessary and making my life hard.
Our new lesson this week was implicit differentiation. Implicit differentiation is when the dependent variable is not isolated and the equation is not a function. You have to derive both sides of the equation, and the derivative of the dependent variable, 'y' in most cases, is a function, so the derivative is dy/dx. It's a great time! And that's only 80% sarcasm! Then, we learned about taking higher order derivatives of implicit equations. So we take the second derivative of the equations. It's pretty straight forward. You just take the derivative and then when you end up with dy/dx, you just substitute in what you just found dy/dx to be!!!!!!! Here's a link to a video explaining implicit differentiation: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-advanced/ab-implicit-diff/v/implicit-differentiation-1
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