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Mathematics 22 Online
OpenStudy (anonymous):

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

OpenStudy (heisenberg):

differentiate y with respect to x, i presume?

OpenStudy (anonymous):

yes with respect to x

OpenStudy (heisenberg):

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

OpenStudy (anonymous):

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

OpenStudy (heisenberg):

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

OpenStudy (heisenberg):

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

OpenStudy (heisenberg):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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?

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