If P(x) = g^2(x), then P'(3) = ?

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Homework Help Overview

The problem involves finding the derivative of a function defined as P(x) = g^2(x) at the point x = 3. The discussion centers around the application of differentiation rules, particularly the chain rule and product rule, in the context of this function.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the interpretation of g^2(x) and its implications for differentiation. There is an exploration of the correct application of the chain rule and product rule in finding the derivative.

Discussion Status

Some participants have provided guidance on the correct differentiation approach, noting the need to apply the chain rule. There is an acknowledgment of the correct interpretation of g^2(x) as g(x) multiplied by itself, leading to further clarification on the derivative expression.

Contextual Notes

Participants express uncertainty regarding the initial interpretation of the function and the differentiation process, indicating a need for clarification on the rules applied. There is also mention of confusion regarding the final answer and the methods used to arrive at it.

Knight226
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Homework Statement


If P(x) = g^2(x), then P'(3) =


Homework Equations





The Attempt at a Solution


I am not quite sure what g^2(x) means...
But my assumption is do the derivative of g^2(x), so it becomes 2g(x), then put the 3 in for x?
so the final answer will be 2g(3) ?
It looks weird to me, so I am not sure if I am doing it correctly or not.

Please advise, thank you.
 
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Almost! you need to apply chain rule!
 
Also, your inclination that g2(x) = g(x)*g(x) is correct.
 
To sutupidmath,
Thank you!
So it should be 2g(x)g'(x), thus the final answer for that question would be P'(3) = 2g(3)g'(3).

To Mark44
I got confused a little there because I thought the final answer was different from 2g(x) (which was the wrong answer anyways). Now I redid the problem using product rule instead for g(x)g(x), and my derivative turned out to be g'(x)g(x) + g(x)g'(x), which is the same as 2g(x)g'(x) anyways :D

Thank you so much to both of you.
 

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