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mathcalculus
 one year 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)?
mathcalculus
 one year 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)?

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

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

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

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2d/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 ?

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

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

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

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

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

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

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2derivative 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 ?

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

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

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

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.12(x^2+y^2)^2=25(x^2y^2)

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

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

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

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

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

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.12(x^2+y^2)^2 dw:1381774415672:dw

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

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2d/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)

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

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

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

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

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

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2d/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?

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1yeah 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

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

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

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

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

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

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

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

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.125(x^2y^2)*(2x2y*dy/dx)

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

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

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

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

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

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

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

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

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

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

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

hartnn
 one year ago
Best ResponseYou've already chosen the best response.24 (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)

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

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