Mathematics
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?

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Latest Questions
xxcoffee: congrats on purple to my self hahah i did ittt
7 seconds ago 22 Replies 2 Medals
walle2037: I need help with the math of 02 Integers
52 seconds ago 6 Replies 1 Medal
jakfishman: help
3 minutes ago 18 Replies 1 Medal
fuyo: what color is a mirror?
1 minute ago 2 Replies 1 Medal
walle2037: what would you do if a babysitter is drunk
15 minutes ago 3 Replies 1 Medal
jackiejackiejack: What has many keys, but can't even open a single door?
18 minutes ago 5 Replies 4 Medals
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!