Derivatives of inverse functions from a table Use the followin...

Question

Derivatives of inverse functions from a table Use the following tables to determine the indicated derivatives or state that the derivative cannot be determined.

b. (f^-1)'(6)

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, and we need to find H inverse of 9. In our table below, we have 3 rows. In the first row in the first column, we have our label X, and in the remaining 5 columns, we have values, and those values are -4, -3, 03, and 4. Our next row is labeled H of X, and it has values in its remaining columns of 8349, and 12. And our last row is labeled H of X, and it has values in its remaining columns of 5 divided by 2452 divided by 7, and 5. We're also given 4 possible choices as our answers. For choice A, we have 2 divided by 7. For choice B, we have 7 divided by 2. For choice C, we have 1 divided by 3, and for choice D, we have 3. Now we're asked to find the derivative, which is H inverse of 9, and we need to evaluate that using the table that we were given. So since we're taking a derivative of the inverse of a function, we need to recall our formula for taking derivatives of inverses of functions. So in our case here, we're going to have H inverse of A. It's going to be equal to 1 divided by H of H inverse of A. Now, in our case, A is going to be equal to 9. So we will, we will have H inverse. of 9. And that is going to be equal to 1 divided by H of H inverse of 9. So we need to use our table to determine the value of H inverse of 9. And so what I'm going to be looking for in our table is when H of X is equal to 9. And that occurs when X is equal to 3. So that means that each inverse of 9. is equal to 3. Since H of 3 is equal to 9. So substituting this value into our expression for H inverse of 9, this is going to be equal to 1 divided by H of 3. And so now we need to use our table to determine the value of H 3. And when X is equal to 3, we see that H of X is equal to 2 divided by 7. So this is going to be equal to 1, divided by the quantity of 2 divided by 7. And we can just simplify this fraction, and so this is going to be equal to. 7 divided by 2. So this is the answer that we were actually looking for, and we compare our answer here to our answer choices. The correct answer choice corresponds to answer choice B. So I hope that this explanation has been useful, and I'll see you in the next video.

Derivatives of inverse functions from a table Use the following tables to determine the indicated derivatives or state that the derivative cannot be determined. <IMAGE>
b. (f^-1)'(6)

Key Concepts

Inverse Functions

Derivative of Inverse Functions

Using Tables for Derivatives

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