Derivatives using tables Let h ( x ) = f ( g ( x ) ) h(x)=f(g(x)) h ( x ) = f ( g ( x )) and p ( x ) = g ( f ( x ) ) p(x)=g(f(x)) p ( x ) = g ( f ( x )) . Use the table to compute the following derivatives. <IMAGE> e. h ′ ( 5 ) h^{\prime}\left(5\right)

Welcome back, everyone. Let F of X be equal to H of G of X. Calculate F at 4 using the following table, and we're given for answer choices AS 5, B 15, C 20, and D 25. So first of all, let's apply the chain rule because F of X is a composite function. The derivative of F of X can be written as the derivative of H. At point G of X multiplied by the derivative of the inner function G of X. And now, if we are looking for F at 4, we're going to replace the axis with 4, right? So we're going to get F at 4 equals H at G of 4 multiplied by G at 0.4. The first thing that we want to find is G at 4. So if we look at the table, we identified G of X at 0.4, it is equal to 0. From here we can simplify the expression F at. 4 is equal to h at.0 multiplied by g at 4. Now we need to find H at 0. If we look at the table, H. 0 is equal to 5. And we also need G at 0.4 and G at.4 is equal to 5. That's it. Now we can substitute these into the expression. So F at. 4 is equal to 5 multiplied by 5. Which gives us 25 and the correct answer to this problem corresponds to the answer choice D 25. Thank you for watching.

2. Intro to Derivatives

Derivatives as Functions

Calculus

2. Intro to Derivatives

Derivatives as Functions

2:15 minutes

Problem 3.7.25eBriggs - 3rd Edition

Textbook Question

Derivatives using tables Let $h(x)=f(g(x))$ and $p(x)=g(f(x))$ . Use the table to compute the following derivatives.
<IMAGE>
e. $h prime of 5$

Verified step by step guidance

Identify the function composition: h(x) = f(g(x)). This is a composition of functions where f is the outer function and g is the inner function.

Recall the chain rule for derivatives, which states that if you have a composition of functions h(x) = f(g(x)), then the derivative h'(x) is given by h'(x) = f'(g(x)) * g'(x).

To find h'(5), substitute x = 5 into the chain rule formula: h'(5) = f'(g(5)) * g'(5).

Use the table to find the values of g(5) and g'(5). Substitute these values into the expression for h'(5).

Next, use the table to find the value of f' at the point g(5). Substitute this value into the expression for h'(5) to complete the calculation.

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Derivatives using tables Let ﻿h(x)=f(g(x))h(x)=f(g(x))h(x)=f(g(x))﻿ and ﻿p(x)=g(f(x))p(x)=g(f(x))p(x)=g(f(x))﻿. Use the table to compute the following derivatives. <IMAGE>e. h′(5)h^{\prime}\left(5\right)

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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>
e. $h prime of 5$