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bmelyk
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I need someone to explain to me step by step the following problem:
 2 years ago
 2 years ago
bmelyk Group Title
I need someone to explain to me step by step the following problem:
 2 years ago
 2 years ago

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bmelyk Group TitleBest ResponseYou've already chosen the best response.1
Find the equation of the tangent line to the curve \[x^{2}y^{2}1=3(x+y)\] at the points (1,1)
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
I have the problem worked out in front of me (prof gave us the answers) but, his work is disorganized and I don't understand what it is he's doing.
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
I figure I have to do this implicitly.
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
yes  you are correct  use implicit differentiation to get an expression for slope of the tangent line at any point (x,y). then substitute x=1, y=1 to find the value of the slope of the tangent line at (1, 1) then use the equation of a straight line: y = mx + c to find c (since you now know m) by using the fact that it passes through the point (1, 1)
 2 years ago

Rezz5 Group TitleBest ResponseYou've already chosen the best response.0
is the answer y=45x?
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
that's not the answer.... the answer is: y=1/5x+4/5
 2 years ago

Rezz5 Group TitleBest ResponseYou've already chosen the best response.0
its a plane....?
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
okay and the way my prof did his differentiation was really weird. his first step looks like: x^{2}2y*y'+y^{2}(2x)=3(1+y')
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
a plane? huh?
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
that's not how i would start the implicit differentiation.
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
\[x^{2}(2y*y')+y^{2}(2x)=3(1+y')\]
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
what your prof did is correct  he is using the product rule, see here: http://www.1728.org/chainrul.htm
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
how would you have done this?
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
haha no idea... i suck at math : (
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
so i use the product rule for x^2*y^2 ??
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
and for the 3*(x+y) ??
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
that is just straight differentiation since it can be written as: 3x + 3y
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
so that will just equal 3y' ??
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
so you can effectively just ignore the 3 outside the braces and just differentiate what is inside the braces
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
so it's 3(1+y')
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
yes  correct
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
okay so now i have the same first line as he does haha.
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
i ignored the 3 outside the brackets because it's a constant right?
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
yes. thats good  you are making progress  maybe you are a lot better at maths than you think. :)
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
haha maybe, maybe not...
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
so now i can take the y^2(2x) over to the other side?
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
and the right hand side over to the left?
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
yes  what you need to do is to get an expression for y'. so move all terms involving y' to the left and the rest to the right
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
first expand the expression on the right
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
do i leave my 3 on the right hand side?
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
snap! yes :)
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
okay so now i have: (x^2)(2y*y')(1y')=3(2xy^2)
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
that look right to you?
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
not quite :(
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
you started with this:\[x^{2}(2y*y')+y^{2}(2x)=3(1+y')\]so first expand the right to get:\[x^{2}(2y*y')+y^{2}(2x)=3+3y'\]then move terms involving y' to the left and the rest to the right to get:\[x^{2}(2y*y')3y'=3y^{2}(2x)\]
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
then factorise y' on the left
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
\[y'=\frac{ 32xy^{2} }{ 2x^{2}y3 }\]
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
woooo. so now that part is done, right?
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
yup  the rest should be straight forward. I need to go for dinner now. I'll check back afterwards to see if you had any further problems.
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
the steps left are: then substitute x=1, y=1 to find the value of the slope of the tangent line at (1, 1) then use the equation of a straight line: y = mx + c to find c (since you now know m) by using the fact that it passes through the point (1, 1)
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
okay thanks. : )
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
yw :) and good luck!
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
i got the rest of it now ; ) thanks a bunch!
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
thats great! and you are more than welcome! :)
 2 years ago
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