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bmelyk
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Looking for someone to check my answer:
Find an equation of the tangent line through the given point.
x 2 y 3 + 15y = 34x, (3, 2)
 one year ago
 one year ago
bmelyk Group Title
Looking for someone to check my answer: Find an equation of the tangent line through the given point. x 2 y 3 + 15y = 34x, (3, 2)
 one year ago
 one year ago

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bmelyk Group TitleBest ResponseYou've already chosen the best response.1
\[\frac{ 342x }{ 2y+15 }\]
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
thats the answer i got.
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
well that's what i had for y'
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
You first need to use implicit differentiation to find an expression for \(\displaystyle\frac{dy}{dx}\). Then substitute x=3 and y=2 into that expression to get the slope of the tangent line at that point. So then you will know the slope of the tangent line and you also know it passes through the point (3,2)  use this information to calculate the equation of the tangent line.
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
was my y' equation correct?
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
it doesn't look correct to me  can you please list your steps so that I can help spot where you may have made a mistake?
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
\[x ^{2}y ^{2}+15y=34x\] \[2x*2yy'+15y'=34\] \[y'(2y+15)=342x\] \[y'=\frac{ 342x }{ 2y+15 }\]
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
I thought you had \(y^3\) in the equation listed in your question?
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
lol so it is.
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
\[y'=\frac{ 342x }{ 3y ^{2}+15 }\]
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
did i have it right the second time (right above what you just wrote)
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
sorry I meant:\[\frac{d}{dx}(x^2y^3)=(x^2)\frac{d}{dx}(y^3)+y^3\frac{d}{dx}(x^2)\]
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
you haven't used the chain rule correctly
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
I mean "product rule"
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
have a look here: http://www.1728.org/chainrul.htm
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
\[x ^{2}*3y ^{2}y'+y ^{3}2x+15y'=34\]
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
that is correct :)
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
okay so now i isolate y'
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
\[y'=\frac{ 342xy ^{3} }{ x ^{2}3y ^{2}+15 }\]
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
yup  now follow the other steps that I had listed above.
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
NOTE: we don't usually write an expression as \(x^23y^2\)  it is better to write it as \(3x^2y^2\)
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
the general rule of thumb is to write in this order: 1. Constants first 2. Then letters in alphabetical order
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
okay so now i sub in my points right?
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
so i had: 14/123
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
perfect! just a couple of more steps to go now :)
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
is the equation: \[y2=14/123x+42/123\]
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
yes  that looks correct. I wouldn't have separated the two constants here (the 2 and the 42/123)
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
you may also want to multiply both sides by 123 to remove the fractions from the final equation.
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
so how would you make it look?
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
ok, you got to this equation:\[y2=14/123x+42/123\]first add 2 to both sides to get:\[y=14x/123 + 288/123\]then multiply both sides by 123  what will you get then?
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
y123=14x+288
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
correct  but again, remember to write constants first  so 123y instead of y123
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
that's not really how you write the equation of a line though.
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
so I would write the final equation as:\[123y=28814x\]
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
it is still an equation of a line. you can write it in "standard form" as follows:\[14x+123y=288\]
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
maybe you are only used to seeing it in the form: \(y=mx +c\)
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
One last advice before I leave  you wrote one of the terms in your original equation as: 14/123x this can sometimes be confused for: \[\frac{14}{123x}\]so it is usually better to write it as: 14x/123
 one year ago
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