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Home Q & A Board Science-Related Homework Help Mathematics
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tootiesmom tootiesmom
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10 years ago
(y/x+8y) = x^7-4 at the point (1, (-3/25))

I need to use implicit differentiation to find the slope of this curve at the given point.  I've been coming up with many funky answers which have not been correct, so any help explaining would be wonderful!
I accidentally wrote the equation wrong.  It should be - y/(x+8y) = x^7-4
y/(x+8y) = x^7-4  this is the correct one no questions about it
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wrote...
#1
10 years ago
Using implicit differentiation:

[(x+8y)y' - y(8y' + 1)]/(x+8y)^2 = 7x^6

Plug in your values of x and y, and solve for y'


Edit: Actually, it's easier if you first multiply through by (x + 8y) to get:

y = (x^7 - 4) * (x + 8y)

Differentiating, you get:

y' = (x^7 - 4) * (1 + 8y') + (7x^6) * (x + 8y)

That's far easier to solve for y' once you plug in your values.
Answer accepted by topic starter
_lani_lani
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#2
Posts: 21
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10 years ago
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