Derivatives using tables Let

Question

Derivatives using tables Let $h(x)=f(g(x))$ and $p(x)=g(f(x))$ . Use the table to compute the following derivatives.

d. $p prime of 2$

Accepted Answer

Welcome back, everyone. Let K of X be equal to G H X. Calculate K at 0.1 using the following table, and we're given our table and for answer choices A -2, B -1, C0, and D2. So essentially for this problem we want to apply the chain rule, right, because K of X is a composite function. So if we want to find the general form of the derivative K of X, we're going to differentiate G H X, right? Because this is how K of X is defined. According to the chain rule, well, essentially, we are going to take the derivative of G with respect to H of X. And then multiply the result by the derivative of the inner function, so H of x. And now if we are looking at X equals 1, then we can say that the derivative of k at 0.1 is simply equal to. The derivative of g at age of 1 we're substituting 1 right multiplied by the derivative of H at 0.1. So now we understand what we want to find, right? First of all, we can see that we need. H.1. So if we look at the table, we can see H of X, and if we look at X equals 1, this gives us a value of 3, right? So let's label our first value that is going to be equal to 3. And this means we can simplify. This expression, we're going to get G. Prime At 0.3 because H at 0.1 is equal to 3, multiplied by H at 0.1. So now we only need to use two values. Let's look at G and let's identify its value at 0.3. According to the table, this is -1. And now each prime at 0.1. Is going to be equal to 2 according to the table, right, so -1. Is multiplied by 2. And this gives us our final result, which is -2, -1 multiplied by 2 is -2. So our final answer corresponds to the answer choice A. Thank you for watching.

Derivatives using tables Let $h(x)=f(g(x))$ and $p(x)=g(f(x))$ . Use the table to compute the following derivatives.
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d. $p prime of 2$

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Derivatives using tables Let $h(x)=f(g(x))$ and $p(x)=g(f(x))$ . Use the table to compute the following derivatives.
<IMAGE>
d. $p prime of 2$