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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)?
 9 months ago
 9 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)?
 9 months ago
 9 months ago

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hartnn Group TitleBest ResponseYou've already chosen the best response.2
could you implicitly differentiate that ?
 9 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=...?
 9 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
what ? where does 2*2 come from ?
 9 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 ?
 9 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
 9 months ago

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
2x+2y?
 9 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 ?
 9 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
if you got that we are almost done :)
 9 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 ?
 9 months ago

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

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
ohman :/
 9 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 ?
 9 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)
 9 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
 9 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 ?
 9 months ago

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

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

hartnn Group TitleBest ResponseYou've already chosen the best response.2
we do find derivative of inside in chain rule, right ?
 9 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.
 9 months ago

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

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

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

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

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

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
oh so then it is. where are we getting x2?
 9 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)
 9 months ago

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
got that =]
 9 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) ?
 9 months ago

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

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
since i have the derivative already?
 9 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?
 9 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
 9 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
 9 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
because there, you have not differentiated x^2+y^2 yrt
 9 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
 9 months ago

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

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

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

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
25(x^2y^2)*(2x2y*dy/dx)
 9 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 ?
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
huh i did?
 9 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)
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
where did i go wrong?
 9 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 ?
 9 months ago

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

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

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

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

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

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

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

hartnn Group TitleBest ResponseYou've already chosen the best response.2
i assume you are simplifying...
 9 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
 9 months ago

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

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
i got 3/119
 9 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)
 9 months ago

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

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

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

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