5. Find dy/dx  in the following:  x^2 + xy + y^2 = 100

Answers (1)

Given function is 
x^2 + xy + y^2 = 100
We can rewrite it as
xy + y^2 = 100 - x^2
Now, differentiation w.r.t. x is
y+\frac{dy}{dx}(x+2y) = \frac{d( 100-x^2)}{dx} = -2x
\frac{dy}{dx} = \frac{-2 x- y}{x+2y}
Therefore, the answer is  \frac{-2 x- y}{x+2y}

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