find dy/dx of
y = (x+y)^2
:/ i dunno how to get the right answer
y = (x+y)^2
:/ i dunno how to get the right answer
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y' = 2(x+y) (1+1y') take dy/dx
y' = 2(x+y + xy' +yy') Multiply
y' = 2x+2y+2xy'+2yy' Distribute
y'-2xy'-2yy' = 2x+2y Move all y' to one side
y'(1-2x-2y) = 2x+2y Factor
y' = (2x+2y)/(1-2x-2y) Solve for y'
y' = 2(x+y + xy' +yy') Multiply
y' = 2x+2y+2xy'+2yy' Distribute
y'-2xy'-2yy' = 2x+2y Move all y' to one side
y'(1-2x-2y) = 2x+2y Factor
y' = (2x+2y)/(1-2x-2y) Solve for y'
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You get on differentiation,
dy/dx = 2(x+y)[1+(dy/dx)]
so {1 - 2(x+y)}dy/dx = 2(x+y)
So dy/dx = 2(x+y)/{1 - 2(x+y)}
dy/dx = 2(x+y)[1+(dy/dx)]
so {1 - 2(x+y)}dy/dx = 2(x+y)
So dy/dx = 2(x+y)/{1 - 2(x+y)}
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y' = 2 ( x + y ) ( 1 + y' )