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## anonymous 5 years ago How do I differentiate ln(xy^2)=y

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1. heisenberg

differentiate y with respect to x, i presume?

2. anonymous

yes with respect to x

3. heisenberg

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

4. 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

5. heisenberg

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

6. heisenberg

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

7. heisenberg

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

8. anonymous

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

9. 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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