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.

c. $p prime of 4$

Accepted Answer

Welcome back, everyone. Let KFX be equal to G H X. Calculate K at point2 using the following table, and we're given for answer choices A -7, B 0, C 14, and D-28. So first of all, let's understand that KFX is a composite function. So its derivative is going to be found using the chain rule. We have to take the derivative of the outer function G at H X and multiply it by the derivative of the inner function, the derivative of H X. And now if we're looking at K at 1.2, it is equal to G at H2 because that's our X multiplied by H at.2. So the first thing that we need to find is H at 0.2, and if we look at the table, H of X intersects with X equals 2 at 2. So H of 2 is equal to 2, right? Now our expression simplifies to K at 0.2 is G at 0.2. Multiplied by H at. 2. Now we need to find G at 0.2 and based on the table, G at. 2 is equal to -4. And we also need H at 0.2. Each prime at 0.2 is equal to 7. So now we can substitute these. K at 0.2 is equal to -4, multiplied by 7, which gives us -28. So the final answer to this problem corresponds to the answer choice D. 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.
<IMAGE>
c. $p prime of 4$

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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>
c. $p prime of 4$