This week in APCalc, we learned about u substitution. U substitution is an easier way to think about doing the Chain Rule. It's easier because you can replace the inside of a function with a variable, then just plug that part of the equation back in where the variable is. I find this useful in more complex equations, but I do not think I need to do it on every problem. It is definitely very useful on problems that have to do a double derivative problem. This is easier because it cleans up a lot of the numbers and replaces it with variables, making the work easier since everything is less cluttered. We also learned about finding the derivative with respect to y when it is not a simple y= problem. You have to take the derivative of each side, using derivative rules when needed. Then you do algebra to get all of the dy/dx's on the same side, then solve for dy/dx. Once you have that equation, you plug in your point to find the slope. What's different about this, is that you have to plug in both x and y into the equation. These problems are the collection of everything we've learned up to this point with derivatives.
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February 2018
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