Lecture Note
University
Rice UniversityCourse
Preparing for the AP Calculus AB ExamPages
1
Academic year
2022
Awayne
Views
66
p {margin: 0; padding: 0;} .ft00{font-size:20px;font-family:Arial;color:#000000;} .ft01{font-size:18px;font-family:Arial;color:#000000;} .ft02{font-size:18px;font-family:ArialMT;color:#000000;} .ft03{font-size:18px;line-height:22px;font-family:Arial;color:#000000;} .ft04{font-size:18px;line-height:22px;font-family:ArialMT;color:#000000;} Quotient Rule for Derivatives The quotient rule is an important derivative application in calculus. It allows us to find thederivative of a quotient of two functions.The quotient rule is not a single equation but rather a collection of related rules that allowus to find derivatives of all kinds of expressions involving division. Let's discuss quotients. The function h of x, which is the rational expression f of x over g of x, can be defined as aquotient. And while there is a proof, it is not worth going into at this point because it would involvethe chain rule, which is a composition of two functions. It will become clear after Section 2.7. I will now give you the formula for finding the derivative of a function involving two otherfunctions, f and g. So the derivative of the function f(x) over the function g(x) is equal to g times f prime minusg prime times f divided by g squared. However, being honest, I do not remember it like this. Because subtraction is notcommutative, I must write the terms in the correct order. Thus, if you flip the signs around, you will get a wrong sign. That’s why I am giving you amnemonic lifehack. This function is called hi because it is, well, on top. And if this is hi, then that must be lo. Thus, the derivative of hi over lo is lo. That is to say, you will take the derivative of what ishi. What do we see? lo d hi minus hi d Lo all over Lo squared. I use that method of organization. I find it easy to remember. Hopefully it is helpful for you. If you have memorized the formula for the quotient rule, you will know when to use it andwhen not to. Why would you not want to use the square root symbol for 1 over x squared, but you dowant to use it for x + 2 ÷ x + 3? It's time to learn about a few new functions, which will allow us to take the derivative ofmore types of functions.
Quotient Rule for Derivatives
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