A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 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)?
anonymous
 3 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)?

This Question is Closed

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

hartnn
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.2what ? where does 2*2 come from ?

hartnn
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.2ok, so now what about d/dx (x^2+y^2) =...?

hartnn
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.2if you got that we are almost done :)

hartnn
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.2we don't rewrite anything

hartnn
 3 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
 3 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)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i get that, but in this problem im confused with why the exponent goes away

hartnn
 3 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 ?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.02(x^2+y^2)^2=25(x^2y^2)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so you're finding the derivative of the inside?

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0my professor also taught us a way of outer first then rewrite inner and then multiple by the derivative of the inner.

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0d/dx[f(g(x))]= f' (g(x))*g'(x)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.02(x^2+y^2)^2 dw:1381774415672:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh so then it is. where are we getting x2?

hartnn
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.2sorry i didn't get your question?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so can it be written like this? : d/dx 4(x^2+y^2) (2x+2y) ?

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0since i have the derivative already?

hartnn
 3 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?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yeah 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0we can't bc we have to leave it as it is right? according to the chain rule

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

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0same for the other side?

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

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.025(x^2y^2)*(2x2y*dy/dx)

hartnn
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.2its like 25x^2  25y^2 derivative = 25(2x)  25 (2y dy/dx)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0where did i go wrong?

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0wait it wasn't because it had no exponent?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0now do we plug in x and y?

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

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i don't know i keep getting the answer wrong whenever i try to submit it

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i keep getting incorrects :/

hartnn
 3 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)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0ohi wrote one of the signs wrong.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.