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

differentiate y with respect to x, i presume?

yes with respect to x

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

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

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

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

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

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

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?