![]() 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. Here is a set of practice problems to accompany the L'Hospital's Rule and Indeterminate Forms section of the Applications of Derivatives chapter of the notes for Paul Dawkins Calculus I course at Lamar University. Use L’Hospital’s Rule to evaluate each of the following limits. All of that over all of that over the denominator function squared. Section 4.10 : L'Hospital's Rule and Indeterminate Forms. 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. Suppose f(pi/3) 4 and f(pi/3) -7, and let g(x) f(x) sin x and. 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. Quotient Rule Questions and Answers Find the derivative of g(x) (x2 -2x + 8)(x3 -8). 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 ![]() Find the tangent line to g(x) x2 +1 x g ( x. Find the tangent line to f (x) 3x54x2 +9x12 f ( x) 3 x 5 4 x 2 + 9 x 12 at x 1 x 1. For problems 21 26 determine where, if anywhere, the function is not changing. The denominator function times V prime of X. For problems 1 20 find the derivative of the given function. 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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