Finding derivatives from a table Find the values of the follow...

Question

Finding derivatives from a table Find the values of the following derivatives using the table.

b. d/dx ((f(x) / g(x)) |x=

Accepted Answer

Hi everyone, let's take a look at this practice problem dealing with derivatives. This problem says to evaluate the following derivative using the table given below. We're asked to find the derivative with respect to X of the quantity of F of X divided by G of X, evaluated at X equal to 2. Below we're given a table that contains 5 rows. In the first row, the first column is labeled X, and the remaining 5 columns have values in them, and they are 2468, and 10. The next row is labeled F of X, and it has values of 5879, and 12. The next row is labeled F of X, and it has values of 658, 12, and 7. The next row is labeled G of X, and it has values of 12, 6, 1917, and 12, and the last row is labeled G of X, and it has values in its columns of 8, 1513, 16, and 19. We're also given 4 possible choices as our answers. For choice A, we have 2 divided by 9, for choice B, we have 1 divided by 18, for choice C, we have 9 divided by 2, and for choice D, we have 18. Now, we're asked to evaluate our derivative using the table that we were given in the problem. So we need to find the derivative. With respect to X, Of the quantity of F of X. Divided by G of X. And this is going to be evaluated at X equal to 2. Now, to take this derivative, we're going to need to use our quotient rule. So here, recall your quotient rule that this is going to be equal to. Here we'll have our denominator, which is G of X, multiplied by the derivative of our numerator, which is F of X. Then we'll have minus our numerator, which is F of X. Multiplied by the derivative of our denominator, which is G of X. And this whole quantity is divided by our denominator squared. It will have the G of X squared in our denominator. This whole fraction is going to be evaluated at X equal to 2. So at this point, we'll do that evaluation. So this is going to be equal to. GF 2. Multiplied by F of 2. Minus F of 2. Multiplied by G of 2. That whole quantity is going to be divided by the quantity of GF2 squared. So now we need to use our table to determine the values for F, F, G, and G of 2. So this is going to be equal to. So the first term we need to evaluate is G2. And so if we look at our table, when X is equal to 2, G of X is going to be equal to 12. So G of 2 is going to be 12, that's going to be multiplied by F2. So looking at our table, when X is 2, F of X is equal to 6, so we'll have 12 multiplied by 6, then we'll have minus F of 2. So, when X is equal to 2, F of X is equal to 5, so we'll have 5, and that gets multiplied by G of 2. And so when X is 2, G of X is going to be equal to 8, so I'll have 5 multiplied by 8. And all of this is divided by G 2 squared. But we already found that GF2 is 12, so we'll have 12 squared on the denominator. So simplifying this expression, this is going to be equal to. We'll have 12 multiplied by 6, which is 72, minus 5 multiplied by 8, which is 40, and that is divided that that quantity is divided by 12 squad, which is 144. So this is going to be equal to. 32 Divided by 144, and when we simplify that fraction, this is going to be equal to 2 divided by 9. So, this is the answer that we are looking for, and when we compare that to our answer choices, the correct answer choice corresponds to answer choice A. So I hope that this explanation has been useful, and I'll see you in the next video.

Finding derivatives from a table Find the values of the following derivatives using the table. <IMAGE>

b. d/dx ((f(x) / g(x)) |x=

Key Concepts

Derivatives

Quotient Rule

Evaluating Derivatives at a Point

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