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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)?
 11 months ago
 11 months 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)?
 11 months ago
 11 months ago

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

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

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

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

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

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

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
ohman :/
 11 months 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 ?
 11 months 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)
 11 months 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
 11 months 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 ?
 11 months ago

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

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

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

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

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

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

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

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

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

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

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
got that =]
 11 months 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) ?
 11 months ago

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

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

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

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

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

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

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

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

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

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
huh i did?
 11 months 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)
 11 months ago

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

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

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

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

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

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

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

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

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

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

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
i got 3/119
 11 months 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)
 11 months ago

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

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

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

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