Question

find dy/dx if ln(xy)=x+y

Answer 1

ln(xy) = chain rule and then a product rule.

Answer 2

how about the left side?

Answer 3

That is the left side

Answer 4

OH OK

Answer 5

:)

Answer 6

^^

Answer 7

Thank you

Answer 8

yw

Answer 9

hint ---> ln(xy) = ln(x) + ln(y) = ln(x) + e^ln(ln(y)) = e^ln(ln(e^ln(y)))) + ln(x)

hope this helps

Answer 10

I still don't get the right answer

Answer 11

Hey mr koala c:
Figure this out yet?

Answer 12

not yet

Answer 13

\[\Large\sf \ln(xy)=x+y\]Derivative of the left side,\[\Large\sf \frac{1}{xy}\color{royalblue}{(xy)'}\]Log gives us one over the stuff right?
Then we have to chain rule, multiplying by the derivative of the inner function.
So we need to differentiate this blue part.
Product rule.\[\Large\sf \frac{1}{xy}\left(\color{royalblue}{x'}y+x\color{royalblue}{y'}\right)\]Make sense so far?

Answer 14

Yay zep :3, always making it look so fancy and nice!

Answer 15

Mr koala i hope you understand how to do it now, with zepdrix's awesome explanation :d

Answer 16

*miamy lmao

Answer 17

I understood Mr Zepdrix, thank you