May I please have help with Implicit Differentiation?

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I have a homework problem that I am unable to get a clear explanation or walkthrough with and I do not understand how to get the final answer. I have been trying for over 2 hours now. The problem is:

4x^2+2xy+2y^2 = 28; (1,3)

Oct 6th, 2015

Thank you for the opportunity to help you with your question!

implicit differentiation means that we differentiate y with respect to x.

therefore, 

simplifying completely then

dy/dx=  -(4x-y)/ (x+2y)

Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 6th, 2015

replacing (1,3)

y'=-(4(1)-3)/ (1+2(3))

y'=-(1)/(1+6)

y'=-1/7

Oct 6th, 2015

Alright, so this is maybe where I keep getting it wrong. I think I do the Rules correctly and I see how you got dy/dx but when I plug in the coordinates to the equation to find the slope, the problem is incorrect after I use the formula: y - y1 = m(x-x1)

Oct 6th, 2015

y' = -1/7

y - 3 = -1/7(x - 1) 

Oct 6th, 2015

dy/dx= -(4x-y)/(x+2y)

for (1,3), then the slope which is change in y over change in x (dy/dx) will be -(4-3)/ (1+6)

then the slope dy/dx= -1/7

Oct 6th, 2015

Here is the algebra that I did.

y - 3 = -1/7x + 1/7

y = -1/7x + 1/7 + 3

y = -1/7x + 1/7 + 21/7

y = -1/7x + 22/7   : mymathlab says this is wrong.

And the problem asks me to "Write the equation for the tangent line in slope-intercept form". 

Oct 6th, 2015

i messed with a sign somewhere,,, please check for this correction: instead of -(8x-2y) it should be -(8x+2y)

therefore dy/dx= -(4+3)/(1+6)

=-7/7

=-1

Sorry for that. 

dy/dx= -1 should give the correct answer.

 please rate my services. Thank you and welcome again.

Oct 6th, 2015

I should have noticed that, sorry. 

Thank you very much for your help. 

Oct 6th, 2015

Welcome. Feel free to leave a message whenever you have a math problem.

Oct 6th, 2015

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