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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

Verified Answer :

Edufirst

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

Answer: option 6. from the list

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