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Damm [24]
3 years ago
11

Calculate dy/dx when xy^3 + y =3x

Mathematics
1 answer:
Yuki888 [10]3 years ago
6 0
The answer is the option D.

You have to use implicit derivative

1) dy / dx = y'

2)

xy^3+y=3x

y^3+3xy^2y'+y'=3

(3xy^2+1)y'=3-y^3

y'= (3-y^3)/(3xy^2+1)

y'=(3-y^3)/(1+3xy^2)


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This question wants you to find a common denominator for the fractions.
This means finding the LCM, least common multiple, for 21 and 9.
This can be done by listing the multiples for each number until they meet at a common one.

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This means the LCM of 21 and 9 is 63.
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