Question

Find dy/dx, using implicit differentiation.
lnx/y = 7 - x

dx/dy =_____

Compare your answer with the result obtained by first solving for y as a function of x and then taking the derivative.
y=____
dx/dy=_____
stuck on all 3 parts on this problem

Answer 1

a little confused
is this
\[\ln(\frac{x}{y})\] or
\[\frac{\ln(x)}{y}\]

Answer 2

the 2nd one ln(x)/y

Answer 3

then quotient rule for this one

Answer 4

\[\frac{y\times \frac{1}{x}-\ln(x)y'}{y^2}=-1\]

Answer 5

\[\frac{y}{x}-\ln(x)y'=-y^2\]
\[-\ln(x)y'=-y^2-\frac{x}{y}\]
\[y'=\frac{y^2}{\ln(x)}+\frac{x}{y\ln(x)}\] if my algebra is right

Answer 6

kk so the first thing you gave me was the dy/dx= correct?

Answer 7

yes

Answer 8

its not taking it for an answer :(

Answer 9

You switched up your x/y's Sat. It should be\[y'=\frac{y^2}{\ln(x)}+\frac{y}{x\ln(x)}\]