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Find (dy)/(dx) in the following:x^2+x y...

Find `(dy)/(dx)` in the following:`x^2+x y+y^2=100`

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`x^2+x y+y^2=100`

Differentiating both sides w.r.t. x.

`(d(x^2+xy+y^2))/dx=(d(100))/dx`

`(d(x^2))/dx+(d(xy))/dx+(d(y^2))/dx=(d(100))/dx`

`2x^(2-1)+(d(xy))/dx+(d(y^2))/dyxxdy/dx=0`

`2x+(d(xy))/dx+(d(y^2))/dyxxdy/dx=0`

`2x+(d(xy))/dx+2y^(2-1).dy/dx=0`

`2x+(d(xy))/dx+2y.dy/dx=0`

Using Product Rule

`2x+((d(x))/(dx).y+(d(y))/dx.x)+2y.dy/dx=0`

`2x+(1.y+x.(d(y))/dx)+2y.dy/dx=0`

`2x+y+x.dy/dx+2y.dy/dx=0`

`(2x+y)+dy/dx.(x+2y)=0`

`dy/dx.(x+2y)=-(2x+y)`

`dy/dx.=-((2x+y))/((x+2y))`
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