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mathcalculus
Group Title
Help:implicit differentiation with a fractions :(
 10 months ago
 10 months ago
mathcalculus Group Title
Help:implicit differentiation with a fractions :(
 10 months ago
 10 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, :)
 10 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
 10 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 ?
 10 months ago

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

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

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

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

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

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

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
in what order, where did you take them?
 10 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
 10 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'
 10 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
2x2+y(x)2=36?
 10 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
 10 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
 10 months ago

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

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
you can't have 36 at the end.
 10 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
 10 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 ??
 10 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
 10 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
 10 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
how did it get simplified to y/18*dy/dx?
 10 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
 10 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
thanks! :) i dontkknow why i missed that silly stuff.
 10 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?
 10 months ago

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

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
the question is asking y'(1)
 10 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)
 10 months ago

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

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