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mathcalculus
Group Title
Help:implicit differentiation with a fractions :(
 9 months ago
 9 months ago
mathcalculus Group Title
Help:implicit differentiation with a fractions :(
 9 months ago
 9 months ago

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myko Group TitleBest ResponseYou've already chosen the best response.0
multiplying everything by 36 you get; 2x^2+y^2=36 which maybe more clear for you, :)
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
hey! :) i tried this: x²/16 + y²/36 = 1 (1/16)x² + (1/36)y² = 1 2(1/16)x + 2(1/36)yy' = 0
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
but so far im not sure what to do after because i know i get x/8 + ?? but then i can't really multiply (1/36) 2y*dy/dx ?
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
isn't the point here to find dy/dx?
 9 months ago

myko Group TitleBest ResponseYou've already chosen the best response.0
let \(F(x,y)=2x^2+y^2=36\) then: \(dF(x,y)=4xdx+2ydy=0\) from here: \(y'=dy/dx=4x/2y=2x/y\)
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
huh? o.o
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
howd you get this?? let F(x,y)=2x2+y2=36
 9 months ago

myko Group TitleBest ResponseYou've already chosen the best response.0
\(dF(x,y)\) is colled full differential it is: \(dF(x,y)=F_xdx+F_ydy\)
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
i never seen that before
 9 months ago

myko Group TitleBest ResponseYou've already chosen the best response.0
\(F_x\) is partial derivative respect to x
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
i know those, but where are the numbers coming from?
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
in what order, where did you take them?
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
i know they're given but how did you get 36 on the other side. and 2x^2+y^2let F(x,y)=2x2+y2=36
 9 months ago

myko Group TitleBest ResponseYou've already chosen the best response.0
ok, other way: think that y is actualy a function of x, so it is y=y(x). Then: \(2x^2+y(x)^2=36\) now we differentiate keeping this in mind 4x+2yy'=0 now just solve for y'
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
2x2+y(x)2=36?
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
yes i know when to differentiate but how did you change the function to that
 9 months ago

myko Group TitleBest ResponseYou've already chosen the best response.0
Ya you right I made a mistake. I was treating 36 like 32, :). Shold be. Rest of steps same. dw:1381788857534:dw
 9 months ago

myko Group TitleBest ResponseYou've already chosen the best response.0
dw:1381789088155:dw
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
i know I was going to tell you.
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
you can't have 36 at the end.
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
i saw a different way on yahoo, would be be able to help me with this one x²/16 + y²/36 = 1 (1/16)x² + (1/36)y² = 1 2(1/16)x + 2(1/36)yy' = 0 (x/8) + (y/18)y' = 0 (y/18)y' = (x/8) y' = (x/8)/(y/18) y' = (x/8)(18/y) y' = (9x/4y) y'(2) = (9(2))/(4(5.2)) y'(2) = 18/20.8 y'(2) = 9/10.4 y'(2) = 0.865
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
I'm not really sure how they got the 4th step :/.... this part> + (y/18)*dy/dx ??
 9 months ago

myko Group TitleBest ResponseYou've already chosen the best response.0
2(1/16)x + 2(1/36)yy' = 0 (2/16)x+(2/36)yy'=0 (x/8) + (y/18)y' = 0
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
yes my question is exactly what you wrote up there .... dw:1381789520628:dw(x/8) + (y/18)y' = 0
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
how did it get simplified to y/18*dy/dx?
 9 months ago

myko Group TitleBest ResponseYou've already chosen the best response.0
your answer is same, just simplify 2 in numerator with 36 in denominator
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
thanks! :) i dontkknow why i missed that silly stuff.
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
then i plug in for x and y and find the common denominators rights?
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
wait we're not done yet! :(
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
i got .005379
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
the question is asking y'(1)
 9 months ago

myko Group TitleBest ResponseYou've already chosen the best response.0
y' = (9x/4y) so: substitute x=1, y=5.80948 y'(1)=9/4(5.80948)
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
okay i got dy/dx=.387298
 9 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
got it thanks @myko :))!
 9 months ago
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