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.

d. d/dx (f(x)³) |x=5

Accepted Answer

Hi everyone, let's take a look at this practice problem dealing with derivatives. This problem says to evaluate the following derivatives using the table given below. We're given the derivative with respect to X of the quantity of G of X rates to the fifth, and it's gonna be evaluated at X equals 10. Below we're given the table that contains 5 rows. The first row is labeled X, and it has 5 columns with values in it, and those values are 2468, and 10. The next row is labeled F of X, and the values in the columns after it are 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, which has values of 8, 1513, 16, and 19. We give 4 possible choices as our answers. For choice A, we have 164,160. For choice B, we have minus 1,969,920. For choice C, we have 1,969,920. And for choice D, we have 1140. Now, the first step we need to do to solve this problem is to take the derivative of the function with respect to X that we were given. And to take this derivative, we will need to apply the chain rule. To recall for the chain rule that we have the derivative with respect to X of the quantity of U of VX. And when we take the derivative of this quantity, this is going to be equal to U of V of X. And that's going to be multiplied by the of X. Where you here is the derivative of view with respect to X and V is the derivative of V with respect to X. And so we're gonna apply the chain rule here to the function that we're given. So, we need to take the derivative with respect to X. Of the quantity of G of X. Raised to the 5th power. And so this is going to be equal to, when I take the derivative of our function G of X rated to the 5th power, I will take the derivative of the quantity rates to the 5th power, so I will have 5 multiplied by that quantity, which in this case is G of X. Raised to the 4th power, and that gets multiplied by the derivative of G of X with respect to X, which is G of X. So now that we have taken our derivative, we need to evaluate this derivative when X equals 0, or X equals to 10, sorry. And so, we can actually use your table to plug in our values for G of X and G of X. So we're going to have 5 multiplied by the quantity of G of X, when X is 10, G of X is equal to 12 in our table. And so that means we'll have 5 multiplied by 12, raised to the 4th power, multiplied by G of X when X is 10, and when we look at the table, G of X is equal to 19 when X is equal to 10. This could get multiplied by 19. And so when we evaluate this expression, this is going to be equal to 1,969,920. And so that is the answer that we're looking for. And if we look at our answer choices, the correct answer choice corresponds to answer choice C. 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>

d. d/dx (f(x)³) |x=5

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Finding derivatives from a table Find the values of the following derivatives using the table. <IMAGE>d. d/dx (f(x)³) |x=5

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

d. d/dx (f(x)³) |x=5