Quotient Rule for Derivatives
The quotient rule is an important derivative application in calculus. It allows us to find the derivative of a quotient of two functions. The quotient rule S not a single equation but rather a collection of related rules that allow us 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 a quotient. And while there is a proof, it is not worth going into at this point because it would involve it the 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 other functions, f and g. So the derivative of the function f(x) over the function g(x) is equal to g times f prime minus g prime times f divided by g squared. However, being honest, I do not remember it like this. Because subtraction is not commutative.: 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 a mnemonic 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 is hi. What do we see? lo d hi minus hi d Lo all over Lo squared. 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 and when not to. Why would you not want to use the square root symbol for 1 over x squared, but you do want 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 of more types of functions. h(x)=f(x)/g(x) d/dx(f(x)/g(x))=(g*f’-g’*f)/g^2 (Lo[dhi]-hi[dLo])/Lo^2
