startanewww
find the derivative of y=(x²+51/x²)²
my steps:
y'=2[x²+5x^(2)](2x+2x)
=4x³+20x4x^(1)
but the answer given is 4x³+20x+20/x³4/x^5
why am i wrong?



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Mimi_x3
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\[y=\left(\frac{x^{2}+51}{x^{2}}\right)^{2} \]??

mukushla
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\[x^2+5\frac{1}{x^2}\]

LeeYeongKyu
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your step was wrong.. at first

startanewww
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why?

lgbasallote
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he's right....

lgbasallote
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well one minor mistake

startanewww
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what have i done wrong?

LeeYeongKyu
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it is derivative of y = (x^2 + 5  1)^2 * (x^2)

lgbasallote
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the derivative of x^(2) is not 2x
it's 2x^3

lgbasallote
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so just change your 2x there with 2x^3 and you're fine. redo the rest of the solution

LeeYeongKyu
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so you use if y = fg y' = f'g + fg'

startanewww
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lgbasallote, i get it, thanks!

lgbasallote
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welcome. also...don't forget you still have a 2 outside..you have to distribute it to the equation too

meer1992
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try use chain rule to solve it

LeeYeongKyu
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the eq is not a ratio..

LeeYeongKyu
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damn..