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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)?
 6 months ago
 6 months ago
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)?
 6 months ago
 6 months ago

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hartnnBest ResponseYou've already chosen the best response.2
could you implicitly differentiate that ?
 6 months ago

hartnnBest ResponseYou've already chosen the best response.2
you will need chain rule here whats d/dx x^2 =...? whats d/dx y^2=...?
 6 months ago

hartnnBest ResponseYou've already chosen the best response.2
what ? where does 2*2 come from ?
 6 months ago

hartnnBest 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 ?
 6 months ago

hartnnBest ResponseYou've already chosen the best response.2
d/dx (x^2) = 2x thats why and the other 2 was already there
 6 months ago

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

hartnnBest 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 ?
 6 months ago

hartnnBest ResponseYou've already chosen the best response.2
if you got that we are almost done :)
 6 months ago

hartnnBest 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 ?
 6 months ago

hartnnBest ResponseYou've already chosen the best response.2
we don't rewrite anything
 6 months ago

hartnnBest 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 ?
 6 months ago

hartnnBest 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)
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
i get that, but in this problem im confused with why the exponent goes away
 6 months ago

hartnnBest ResponseYou've already chosen the best response.2
ok, you said d/dx (x^2) = 2x why did the exponent go away here ?
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
2(x^2+y^2)^2=25(x^2y^2)
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
so you're finding the derivative of the inside?
 6 months ago

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

mathcalculusBest 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.
 6 months ago

hartnnBest ResponseYou've already chosen the best response.2
he must have meant "derivative of outer first ....."
 6 months ago

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

mathcalculusBest ResponseYou've already chosen the best response.1
2(x^2+y^2)^2 dw:1381774415672:dw
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
oh so then it is. where are we getting x2?
 6 months ago

hartnnBest 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)
 6 months ago

hartnnBest ResponseYou've already chosen the best response.2
sorry i didn't get your question?
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
so can it be written like this? : d/dx 4(x^2+y^2) (2x+2y) ?
 6 months ago

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

mathcalculusBest ResponseYou've already chosen the best response.1
so i get rid of it?
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
since i have the derivative already?
 6 months ago

hartnnBest 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?
 6 months ago

mathcalculusBest 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
 6 months ago

mathcalculusBest 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
 6 months ago

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

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

mathcalculusBest ResponseYou've already chosen the best response.1
now what do we do
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
same for the other side?
 6 months ago

hartnnBest ResponseYou've already chosen the best response.2
yes, other side is too simple. try ?
 6 months ago

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

mathcalculusBest ResponseYou've already chosen the best response.1
25(x^2y^2)*(2x2y*dy/dx)
 6 months ago

hartnnBest ResponseYou've already chosen the best response.2
what why ? we need chain rule for just y^2 here, isn't it ?
 6 months ago

hartnnBest ResponseYou've already chosen the best response.2
its like 25x^2  25y^2 derivative = 25(2x)  25 (2y dy/dx)
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
where did i go wrong?
 6 months ago

hartnnBest ResponseYou've already chosen the best response.2
the x^2y^2 part was unnecessary, you though it was chain rule again ?
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
wait it wasn't because it had no exponent?
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
now do we plug in x and y?
 6 months ago

hartnnBest ResponseYou've already chosen the best response.2
correct! put x=3, y=1 in that...
 6 months ago

hartnnBest ResponseYou've already chosen the best response.2
i assume you are simplifying...
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
i don't know i keep getting the answer wrong whenever i try to submit it
 6 months ago

hartnnBest ResponseYou've already chosen the best response.2
what did u get for dy/dx ?
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
i keep getting incorrects :/
 6 months ago

hartnnBest 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)
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
ohi wrote one of the signs wrong.
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
thank you so much!
 6 months ago
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