M.Uzair U.

asked • 12/13/16

Find dy/dx if. x^2 = x-y/x+y

Find dy/dx if.         x^2 = x-y/x+y

Kenneth S.

Serious question: Did the student INTEND the right side of this equation to be(x-y) / (x+y) ??
 
If so, the solution would be very different from that given by Gregg K.
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12/13/16

Gregg K.

tutor
Good point Ken
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12/13/16

Gregg K.

tutor
If the right side is (x-y)/(x+y)
 
x^3 + x^2y = x - y

3x^2 + 2xy +x^2y' = 1-y'

y' = -(3x^2+2xy-1)/(1+x^2)
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12/13/16

1 Expert Answer

By:

Gregg K. answered • 12/13/16

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My first step probably would be to multiply both sides of the equation by x, this would help us avoid the quotient rule.
 
x^3 = x^2 - y + xy
 
 
We now will differentiate each term with respect to x and apply the chain rule to y as we will treat them as unknown functions of x.
 
3x^2 = 2x -dy/dx + y +x(dy/dx)
 
Now we will isolate our dy/dx
 
3x^2 -2x -y = dy/dx(x-1)
 
(3x^2-2x-y)/(x-1) = dy/dx
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M.Uzair U.

If we want to apply quotient rule then how could this solve
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12/13/16

Gregg K.

tutor
x^3 + x^2y = x - y
 
3x^2 + 2xy +x^2y' = 1-y'
 
y' = -(3x^2+2xy-1)/(1+x^2)
 
 
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12/13/16

Gregg K.

tutor
The above is not quotient rule applied, I was just replying to Ken
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12/13/16

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