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Differentiation H/W :(

Sc0tt

Posted 07 December 2008 - 12:22 PM

Hey everyone, i really hope you can help me.

I have once again left my homework too late to ask for help with, its due in tomorrow..
Seemed to have done it all pretty well apart from this question.. Its stumping me real bad.

y=2√x(x+2).
Find dy/dx.

Really hope you can help me here.
Thanks everyone in advance.

Scott.

Marcus

Posted 07 December 2008 - 01:04 PM

Right, I assume the equation is  y=2\sqrt{x(x+2)} not  y=2\sqrt{x}\times(x+2) but if I got this wrong just post again
This is a chain rule question,
 y=2\sqrt{x(x+2)} //first you have to multiply out the inside of the root , I've also changed the root to a power of 1/2
y=2(x^{2}+2x)^{1/2} //so dy/dx is equal to the derivative of the brackets multiplied by the derivative of the inside, check the notes on hsn if you don't know how to differentiate using the chain rule
\frac{dy}{dx}=(x^{2}+2x)^{-1/2} \times (2x+2) //then just simplify a bit
\frac{dy}{dx}=\frac{2(x+1)}{\sqrt{x(x+2)}}

Hope this helps

x-lisa

Posted 07 December 2008 - 03:53 PM

Hi

I would probably do it like x^1/2 (x to the power 1/2)
so it would be x^1/2(x+2)
= x^3/2 + 2x^1/2

so dy/dx = 3/2x^1/2 + x^-1/2

hope it helps =]

Sc0tt

Posted 07 December 2008 - 04:09 PM

Ahh thanks very much guys, both methods have really helped me understand differentiation much much better biggrin.gif

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