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mathcalculus
 2 years ago
Help:implicit differentiation with a fractions :(
mathcalculus
 2 years ago
Help:implicit differentiation with a fractions :(

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

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

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0but 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 ?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0isn't the point here to find dy/dx?

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

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

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

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i never seen that before

myko
 2 years ago
Best ResponseYou've already chosen the best response.0\(F_x\) is partial derivative respect to x

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i know those, but where are the numbers coming from?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0in what order, where did you take them?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i 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

myko
 2 years ago
Best ResponseYou've already chosen the best response.0ok, 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'

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0yes i know when to differentiate but how did you change the function to that

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

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i know I was going to tell you.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0you can't have 36 at the end.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i 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

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

myko
 2 years ago
Best ResponseYou've already chosen the best response.02(1/16)x + 2(1/36)yy' = 0 (2/16)x+(2/36)yy'=0 (x/8) + (y/18)y' = 0

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

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0how did it get simplified to y/18*dy/dx?

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

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0thanks! :) i dontkknow why i missed that silly stuff.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0then i plug in for x and y and find the common denominators rights?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0wait we're not done yet! :(

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0the question is asking y'(1)

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

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0okay i got dy/dx=.387298

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0got it thanks @myko :))!
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