Find the slope of the line tangent to the
graph of ln(xy)-2x=0 when x= -1

answer choices..
1. slope = 3/2e^-2
2. slope= 3/2e^2
3. slope= 3e^-2
4. slope= -3e^2
5. slope= -3/2e^2
6. slope= -3e^-2

Ln(xy) - 2x =0

slope of the tangent line = derivative of the function

[ln(xy)]' = [2x]'

[1/(xy)] [y + xy'] = 2

y + xy' = 2(xy)

xy' = 2xy - y =y(2x-1)

y' = y(2x-1)/x

Now use x = -1 to find y and after to find y'

ln(xy) = 2x
x=-1
ln(-y) =-2

-y = e^-2

y = - e^-2

y' = [-e^-2][2(-1)-1]/(-1) = [e^-2](-2-1)= [e^-2](-3) = - 3e^-2

option 6. from the list

Step 1: 6x-10=1; step 2: 6x=11