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mathcalculus
Group Title
Help:implicit differentiation with a fractions :(
 one year ago
 one year ago
mathcalculus Group Title
Help:implicit differentiation with a fractions :(
 one year ago
 one year 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, :)
 one year 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
 one year 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 ?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
isn't the point here to find dy/dx?
 one year 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: \(y'=dy/dx=4x/2y=2x/y\)
 one year ago

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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