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bmelyk
 3 years ago
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)
bmelyk
 3 years ago
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)

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bmelyk
 3 years ago
Best ResponseYou've already chosen the best response.1\[\frac{ 342x }{ 2y+15 }\]

bmelyk
 3 years ago
Best ResponseYou've already chosen the best response.1well that's what i had for y'

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.1You 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.

bmelyk
 3 years ago
Best ResponseYou've already chosen the best response.1was my y' equation correct?

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.1it 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?

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

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

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

bmelyk
 3 years ago
Best ResponseYou've already chosen the best response.1did i have it right the second time (right above what you just wrote)

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

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.1you haven't used the chain rule correctly

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.1have a look here: http://www.1728.org/chainrul.htm

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

bmelyk
 3 years ago
Best ResponseYou've already chosen the best response.1okay so now i isolate y'

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

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.1yup  now follow the other steps that I had listed above.

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

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

bmelyk
 3 years ago
Best ResponseYou've already chosen the best response.1okay so now i sub in my points right?

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.1perfect! just a couple of more steps to go now :)

bmelyk
 3 years ago
Best ResponseYou've already chosen the best response.1is the equation: \[y2=14/123x+42/123\]

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

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.1you may also want to multiply both sides by 123 to remove the fractions from the final equation.

bmelyk
 3 years ago
Best ResponseYou've already chosen the best response.1so how would you make it look?

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.1ok, 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?

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.1correct  but again, remember to write constants first  so 123y instead of y123

bmelyk
 3 years ago
Best ResponseYou've already chosen the best response.1that's not really how you write the equation of a line though.

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

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

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

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.1One 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
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