8/24/2023 0 Comments Ap calculus chain rule quiz![]() ![]() Derivative of g of x to the n is n g of x to the n-1 times g prime of x. So don't forget the general power rule is just a specific special case of the chain rule. That's negative 42 x squared oops minus because I have to distribute the negative 7 over these 2 terms so negative 7 times 3 is negative 21 and that's my answer. And in the numerator I'll have negative 7 times 6x squared plus 3. So I have a fraction and I'll have 2x cubed plus 3x-1 to the eighth power. And so let's make the observation that this quantity here because I have a negative 8 exponent it's going to end up in the denominator. So according to this rule h prime is going to be the derivative of this and so I take this n the exponent pull out in front so I get negative 7 times this quantity 2x cubed plus 3x-1.Īnd the new exponent is going to be the old exponent minus 1, so negative 7-1 is negative 8 times and then the derivative of the inside function and that's going to be 6x squared plus 3 I'll put that here and your teacher may want you to simplify this. So this is the inside function, so equals and the outside function is the raising to the negative 7 that's the outside function and inside I'll make blue 2x cubed plus 3x-1. Like if I were going to plug 5 into this function I'd raise 5 to the third power multiply by 2 add 3 times 5, I'd be working on this part of the function. Usually the best way to identify inside versus outside is to think about calculating values. Because its so tough Ive divided up the chain rule to a bunch of sort of sub-topics and I want to deal with a bunch of special cases of the chain rule, and this one is going to be called the general power rule. 45 minutes per week in class, and maybe some time outside of. The chain rule is one of the toughest topics in Calculus and so dont feel bad if youre having trouble with it. ![]() This one-time class will contain 35 mins of lecture time and then 15 mins of students' activities (worksheet problem solving). And so just to be absolutely clear I'm going to color code this function so that we can see what's the inside function and what's the outside function. We are going to work on solving some Calculus questions with the application of Chain Rule. This is just a special case of the chain rule, so let's try it out on this function h of x equals this function 2x cubed plus 3x-1 all raised to the negative 7 power. So the derivative of g of x to the n is n times g of x to the n minus 1 times the derivative of g of x. So how do you differentiate one these well we're going to use a version of the chain rule that I'm calling the general power rule. Anyway this is the chain rule I want to introduce you to what I'm calling a general power function so h of x is the general power function if it could be written as some function g of x any function raised to the nth power. We'll get into that in a second, the call with the chain rule is it's a method for differentiating composite functions like f of g of x and I've been in a habit of color coding my composite functions so that the inside part is blue and the outside part is red. Because it's so tough I've divided up the chain rule to a bunch of sort of sub-topics and I want to deal with a bunch of special cases of the chain rule, and this one is going to be called the general power rule. FREE.The chain rule is one of the toughest topics in Calculus and so don't feel bad if you're having trouble with it. It is meant to give students a taste of the types of problems they will see in the new AP Precalculus course right from the very beginning. It containsĤ6 qui zzes in the style of the AP exam with 4 multiple choice and 1 free response problem for e ach topic. This is a companion piece to the AP Precalculus Manual. The other units are being written this summer with unit 2 available at the end of August and unit 3 available at the end of September. This is a set of FREE quizzes and exams plus a comprehensive 2-part exam. Using the AP Precalculus manual framework, available are Classroom Exams for Unit 1. Teachers can use it to completely teach the course with ready-made lesson plans complete with classwork and homework. The MMM manual is a full course t hat mirrors the framework of the new course. This c ourse is meant to prepare students for the rigors of Calculus in college. The College Board is instituting a new AP Precalculus course in the fall of 2023. It is highly entertaining and those students who have been on cruises will relate to just about every situation described and those who haven't will want to take a cruise. There problems are about food, entertainment, getting around the ship, entertainment, shore excursions, and just about every aspect of the ship. ![]() But the kicker is that these problems were written about and aboard a cruise ship. This summer venture from MMM is a 40-problem set of of free response questions in th e style of the AP Exam.
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