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mathcalculus
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.2could you implicitly differentiate that ?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

hartnn
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1ohi wrote one of the signs wrong.

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