But if you don't know the chain rule yet, this is fairly useful. But you could also do the quotient rule using the product and the chain rule that you might learn in the future. Now what you'll see in the future you might already know something called the chain rule, or you might You could try to simplify it, in fact, there's not an obvious way Plus, X squared X squared times sine of X. This is going to be equal to let's see, we're gonna get two X times cosine of X. Actually, let me write it like that just to make it a little bit clearer. So that's cosine of X and I'm going to square it. All of that over all of that over the denominator function squared. The derivative of cosine of X is negative sine X. The product rule and the quotient rule further questions 07b. Minus the numerator function which is just X squared. Book your place now Cheat Sheets Questions by Topic Worksheets. V of X is just cosine of X times cosine of X. So it's gonna be two X times the denominator function. So based on that F prime of X is going to be equal to the derivative of the numerator function that's two X, right over Of X with respect to X is equal to negative sine of X. So that is U of X and U prime of X would be equal to two X. Well what could be our U of X and what could be our V of X? Well, our U of X could be our X squared. So let's say that we have F of X is equal to X squared over cosine of X. Theyre very useful because the product rule gives you the derivatives for the product of two functions, and the quotient rule does the same for the quotient of two functions. We would then divide by the denominator function squared. The product rule and the quotient rule are a dynamic duo of differentiation problems. Get if we took the derivative this was a plus sign. If this was U of X times V of X then this is what we would The denominator function times V prime of X. Its going to be equal to the derivative of the numerator function. Then the quotient rule tells us that F prime of X is going to be equal to and this is going to lookĪ little bit complicated but once we apply it, you'll hopefully get a little bit more comfortable with it. So for example if I have some function F of X and it can be expressed as the quotient of two expressions. But here, we'll learn about what it is and how and where to actually apply it. It using the product rule and we'll see it has some Quotient Rule Derivative Practice and Quotient Rule Derivative Solutions. In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature. Going to do in this video is introduce ourselves to the quotient rule. The Quotient Rule mc-TY-quotient-2009-1 A special rule, thequotientrule, exists for dierentiating quotients of two functions.
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