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

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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.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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