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Need Help! Very confused on this!

#1 User is offline   Nancie Icon

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Posted 10 December 2008 - 04:01 PM

Given that

Y =
3X³ + X
X²

Find
dy
dx


How do I go about doing this and were do I start?!
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#2 User is offline   Marcus Icon

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Posted 10 December 2008 - 04:31 PM

to do this you have to split up the fraction
ie \frac{3x^{3}+x}{x^{2}}=\frac{3x^{3}}{x^{2}} + \frac{x}{x^{2}} this can then be simplified to form a polynomial which can then be differentiated

just reply if you want me to go through this in more detail
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#3 User is offline   SockRock16 Icon

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Posted 14 December 2008 - 04:47 PM

Ok, every one else may understand this but I don't! Please help me with the next steps!
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#4 User is offline   Marcus Icon

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Posted 14 December 2008 - 05:41 PM

the next steps to solve this are:

y=\frac{3x^{3}+x}{x^{2}}=\frac{3x^{3}}{x^{2}} + \frac{x}{x^{2}}
now we can simplify these fractions as there are 'x's on top and bottom of the fractions
y=3x+\frac{1}{x}=3x+x^{-1} //then just differentiate each term
\frac{dy}{dx}=3-x^{-2} \\then you can rearrange if you want, but this would be an acceptable final answer
\frac{dy}{dx}=3-\frac{1}{x^{2}}=\frac{3x^{2}-1}{x^{2}}
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