anonymous
  • anonymous
how do you find the derivative of (y+4)/(x-2)=5y at (3,1)???
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
either solve for "y" all by its little lonesome; or use implicit deriv..different.....that one word...
amistre64
  • amistre64
lets try implicit... 5y = (y+4)/(x-2) ; take the d/dx of both sides.. (d/dx)(5y) = (d/dx)[(y+4)/(x-2)]
amistre64
  • amistre64
5y' = apply quotient rule to this side 5y' = [(x-2)(1y') - (y+4)(x')] / [(x-2)^2] ; dy/dx = y' ; x' = 1

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amistre64
  • amistre64
get y' by itself if you dare :)
anonymous
  • anonymous
no easier way? how can you get y by it self
amistre64
  • amistre64
lol.... I get: y+4 y' = ------ x-7
anonymous
  • anonymous
how??
amistre64
  • amistre64
plug in (3,1) y' = -5/6 ?? where did I lose ya? :)
amistre64
  • amistre64
y' = -5/4 ; forgot how to add lol
anonymous
  • anonymous
how did you get to y+4/x-7
amistre64
  • amistre64
by using paper and pencil really... but lets see if I can type it out...
amistre64
  • amistre64
(x-2)(1y') - (y+4)(x') 5y' = ---------------- ; move (x-2)^2 up and bring y' down.. (x-2)^2 (x-2)(y') - (y+4) 5(x-2)^2 = ---------------- ; split the fraction.... y' (x-2)(y') (y+4) 5(x-2)^2 = ------- - ------- ; cancel top to bottom your y' y' y' (y+4) 5(x-2)^2 = (x-2) - ------- ; now subtract (x-2) from both sides y' - (y+4) [5(x-2)^2]-(x-2) = ------- ; I forgot something on the paper.... y'
amistre64
  • amistre64
regardless tho, lets work this out: -4-y y' = ---------------- [5(x-2)^2] - (x-2) try that one :)
amistre64
  • amistre64
(x=3,y=1) y' = (-4-1) / [5(3-2)^2 - (3-2)] y' = -5 / 4 , is that right?
amistre64
  • amistre64
HAH!!! I got the same answer as I did with the last one lol
anonymous
  • anonymous
yessss thank you so much

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