Question

How do I differentiate ln(xy^2)=y

Answer 1

differentiate y with respect to x, i presume?

Answer 2

yes with respect to x

Answer 3

my first instinct says try implicit differentiation, but u substitution could be an option.

Answer 4

It is an implicit differentiation problem, however I can't figure out what ln(xy^2) differentiates to... if I could figure that out I could simplify it algebraically no problem

Answer 5

\[\frac{\delta y}{\delta x} \ln(xy^2) = y^2 * \frac{\delta}{\delta x} (x)\]

Answer 6

so since we are differentiating with respect to x, we can consider any 'y' portions to be constant and proceed as such.

Answer 7

but for implicit differentiation, you have to include a dy/dx term when you take the derivative

Answer 8

thank you! That helps me understand how to finish the problem much better!

Answer 9

The derivative is implicit, but it also requires chain rule (because xy^2 is a function) and, later, product rule (x times y^2). The right hand side is just dy/dx. That help?

Answer 10

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Answer 11

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Answer 12

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Answer 13

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Answer 14

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Answer 15

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Answer 17

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Answer 18

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Answer 19

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Answer 20

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Answer 21

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Answer 22

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Answer 23

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a.
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b.

Answer 24

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Answer 25

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Answer 26

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Answer 27

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Answer 28

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Answer 29

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