Prove that the the DERIVATIVE of p(x) is ?

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Homework Help Overview

The discussion revolves around finding the derivative of the function p(x) = (2x+8) / (√x). Participants are tasked with proving that p'(x) equals (x√x - 4√x)/x.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants express difficulty in simplifying the derivative and question the correctness of the provided answer. There are attempts to apply the product and chain rules, with some participants seeking clarification on algebraic simplification techniques.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and questioning the validity of the given answer. Some guidance has been offered regarding algebraic manipulation, but no consensus has been reached on the correct approach or solution.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the extent of guidance they can receive. There is a focus on matching a specific answer format, which adds to the complexity of the discussion.

Stanc
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Prove that the the DERIVATIVE of p(x) is...?

Homework Statement



If p(x) = (2x+8) / (√x) Prove that p'(x) is (x√x - 4√x)/x


The Attempt at a Solution



I keep getting stumped, I cannot simplify it down
 
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Stanc said:

Homework Statement



If p(x) = (2x+8) / (√x) Prove that p'(x) is (x√x - 4√x)/x


The Attempt at a Solution



I keep getting stumped, I cannot simplify it down

Well, what's your answer? Show your work. I think the given answer is wrong.
 
Dick said:
Well, what's your answer? Show your work. I think the given answer is wrong.

Heres what I got: (2x+8)(-1/2) [x^(-3/2)] + {x^(-1/2)} (2) but from here I don't know where to go...
 
You can try simplifying it algebraically. Remember, you are trying to match a given answer.
 
SteamKing said:
You can try simplifying it algebraically. Remember, you are trying to match a given answer.

What do you mean by simplifying it algebraically?? Can you give me a start?
 
Stanc said:
What do you mean by simplifying it algebraically?? Can you give me a start?

You want to write it as (something)/x. Multiply what you've got by x/x.
 

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