Question

find y' if lnxy = x+ y. I have a lot of questions similar to this on my hw, so an explanation of why you divide/multiply ect. would be tremendous help! Thanks!

Answer 1

lnxy = lnx +lny
replace and make y is in left side, x is in right side, then take derivative both sides to get the answer

Answer 2

remember when taking derivative of "y" term to multiply by dy/dx or y'

Answer 3

\[\ln x + \ln y = x+y\]
\[\rightarrow \frac{1}{x} + \frac{1}{y} y' = 1 + 1y'\]
solve for y'
\[\frac{1}{y} y' - y' = 1 - \frac{1}{x}\]
\[y'(\frac{1}{y} - 1) = 1 - \frac{1}{x}\]
\[y'=\frac{ 1 - \frac{1}{x}}{\frac{1}{y}-1}\]

Answer 4

lol, I see what you were saying now ooops. Thank you dumbcow!

Answer 5

yw i figured i would give the solution so you have an example to use for your other problems
the steps are usually the same
-take derivative
-solve for y'