anonymous
  • anonymous
How do I differentiate ln(xy^2)=y
Mathematics
schrodinger
  • schrodinger
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heisenberg
  • heisenberg
differentiate y with respect to x, i presume?
anonymous
  • anonymous
yes with respect to x
heisenberg
  • heisenberg
my first instinct says try implicit differentiation, but u substitution could be an option.

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anonymous
  • 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
heisenberg
  • heisenberg
\[\frac{\delta y}{\delta x} \ln(xy^2) = y^2 * \frac{\delta}{\delta x} (x)\]
heisenberg
  • heisenberg
so since we are differentiating with respect to x, we can consider any 'y' portions to be constant and proceed as such.
heisenberg
  • heisenberg
but for implicit differentiation, you have to include a dy/dx term when you take the derivative
anonymous
  • anonymous
thank you! That helps me understand how to finish the problem much better!
anonymous
  • 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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