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. Minus the numerator function which is just X squared. 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. We would then divide by the denominator function squared. 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 Going to do in this video is introduce ourselves to the quotient rule.
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