# Thread: Derivative, Chain Rule Problem. Help Plz!!

1. ## Derivative, Chain Rule Problem. Help Plz!!

The question is asking to find the first derivative of the composition (fogoh)(x). Given:

$\displaystyle f(x) = \sqrt{x^2-1}$
$\displaystyle g(x) = (x^3+5)^{17}$
$\displaystyle h(x) = \frac{2}{x}$

Computing for the derivatives I got:

$\displaystyle f'(x) = \tfrac{1}{2}(x^2-1)^{\frac{-1}{2}}(2x)$
$\displaystyle g'(x) = 17{(x^3+5)}^{16}(3x)$
$\displaystyle h'(x) = -2(2x)$

I understand that the derivative of $\displaystyle f(g(h(x))) = [f'(g(h(x)))].[g'(h(x))].[h'(x)]$ so I just need to plug the functions but I am not getting the right answer. Can someone please take me through the process step by step so I can see where I went wrong? I understand this is a long question but it would be greatly appreciated! Thank you!

2. f ' is correct but g ' and but h ' aren't

g= (x^3 + 5)^17

g ' = 17(x^3 +5)^16 (3x^2)

h = 2/x = 2x^(-1)

h' = -2 x^(-2) = -2/(x^2)

Try it now
The text contains a mathematical question related to finding the first derivative of a composition of functions using the chain rule. It also provides an answer that corrects the derivatives of the functions g and h.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Thread: Derivative, Chain Rule Problem. Help Plz!!

1. ## Derivative, Chain Rule Problem. Help Plz!!

The question is asking to find the first derivative of the composition (fogoh)(x). Given:

$\displaystyle f(x) = \sqrt{x^2-1}$
$\displaystyle g(x) = (x^3+5)^{17}$
$\displaystyle h(x) = \frac{2}{x}$

Computing for the derivatives I got:

$\displaystyle f'(x) = \tfrac{1}{2}(x^2-1)^{\frac{-1}{2}}(2x)$
$\displaystyle g'(x) = 17{(x^3+5)}^{16}(3x)$
$\displaystyle h'(x) = -2(2x)$

I understand that the derivative of $\displaystyle f(g(h(x))) = [f'(g(h(x)))].[g'(h(x))].[h'(x)]$ so I just need to plug the functions but I am not getting the right answer. Can someone please take me through the process step by step so I can see where I went wrong? I understand this is a long question but it would be greatly appreciated! Thank you!

2. f ' is correct but g ' and but h ' aren't

g= (x^3 + 5)^17

g ' = 17(x^3 +5)^16 (3x^2)

h = 2/x = 2x^(-1)

h' = -2 x^(-2) = -2/(x^2)

Try it now
user
The text contains a mathematical question related to finding the first derivative of a composition of functions using the chain rule. It also provides an answer that corrects the derivatives of the functions g and h.

TYPE: SINGLE_QUESTION_WITH_ANSWER