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mathcalculus
Group Title
Find the slope of the tangent line to the curve (a lemniscate) 2(x^2+y^2)^2=25(x^2y^2) at the point (3,1)?
 one year ago
 one year ago
mathcalculus Group Title
Find the slope of the tangent line to the curve (a lemniscate) 2(x^2+y^2)^2=25(x^2y^2) at the point (3,1)?
 one year ago
 one year ago

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hartnn Group TitleBest ResponseYou've already chosen the best response.2
could you implicitly differentiate that ?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
you will need chain rule here whats d/dx x^2 =...? whats d/dx y^2=...?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
what ? where does 2*2 come from ?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
d/dx[2(x^2+y^2)^2] = 2*(2 (x^2+y^2)) times d/dx(x^2+y^2) this is because of chain rule, got this step ?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
d/dx (x^2) = 2x thats why and the other 2 was already there
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
ok, so now what about d/dx (x^2+y^2) =...?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
2x+2y?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
here, chain rule again comes into picture d/dx f(y) = f'(y) dy/dx so d/dx (y^2) = 2y dy/dx got this ?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
if you got that we are almost done :)
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
d/dx[2(x^2+y^2)^2] = 2*(2 (x^2+y^2)) times d/dx(x^2+y^2) this part ?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
whats d/dx x^2 =.... ?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
we don't rewrite anything
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
ohman :/
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
derivative of outer times derivative of inner like for (sin x)^3 we have outer = x^3, derivative = 3x^2 inner = sin x derivative = cos x so, 3 (sin x)^2 cos x got this ?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
in same way d/dx [(x^2+y^2)^2] = 2 (x^2+y^2) times d/dx (x^2+y^2)
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
i get that, but in this problem im confused with why the exponent goes away
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
ok, you said d/dx (x^2) = 2x why did the exponent go away here ?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
2(x^2+y^2)^2=25(x^2y^2)
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
so you're finding the derivative of the inside?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
we do find derivative of inside in chain rule, right ?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
my professor also taught us a way of outer first then rewrite inner and then multiple by the derivative of the inner.
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
he must have meant "derivative of outer first ....."
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
d/dx[f(g(x))]= f' (g(x))*g'(x)
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
yes, here f(x) was x2
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
well isn't it 4?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
2(x^2+y^2)^2 dw:1381774415672:dw
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
yes, it is 4.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
oh so then it is. where are we getting x2?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
d/dx[2(x^2+y^2)^2] = 2*(2 (x^2+y^2)) times d/dx(x^2+y^2) = 4(x^2+y^2)times d/dx(x^2+y^2)
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
sorry i didn't get your question?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
got that =]
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
so can it be written like this? : d/dx 4(x^2+y^2) (2x+2y) ?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
no, why would d/dx come in front again ?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
so i get rid of it?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
since i have the derivative already?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
d/dx [(x^2+y^2)^2] = 2 (x^2+y^2) times d/dx (x^2+y^2) = 4 (x^2+y^2) times (2x+2y dy/dx) see whether you get this?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
yeah i got it, but why don't we do dy/dx here: 4 (x^2+y^2) times (2x+2y dy/dx)dw:1381774790286:dw
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
we can't bc we have to leave it as it is right? according to the chain rule
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
because there, you have not differentiated x^2+y^2 yrt
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
and yes, we need to leave it as it is, that too
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
now what do we do
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
same for the other side?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
yes, other side is too simple. try ?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
right side is just 25(2x2y dy/dx) isn't it ?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
25(x^2y^2)*(2x2y*dy/dx)
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
what why ? we need chain rule for just y^2 here, isn't it ?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
huh i did?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
its like 25x^2  25y^2 derivative = 25(2x)  25 (2y dy/dx)
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
where did i go wrong?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
the x^2y^2 part was unnecessary, you though it was chain rule again ?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
wait it wasn't because it had no exponent?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
yes, correct.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
25*(2x2y*dy/dx)
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
so its this?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
got cha.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
now do we plug in x and y?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
correct! put x=3, y=1 in that...
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
i assume you are simplifying...
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
i don't know i keep getting the answer wrong whenever i try to submit it
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
what did u get for dy/dx ?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
i keep getting incorrects :/
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
i got 3/119
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
4 (x^2+y^2) times (2x+2y dy/dx) = 25(2x2y dy/dx) x=3, y=1 4(9+1) (6 +2 dy/dx) = 25 (6 2 dy/dx)
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
ohi wrote one of the signs wrong.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
got it.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
thank you so much!
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
welcome ^_^
 one year ago
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