Implicit tangent slope

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Problem

The curve $x^2+xy+y^2=7$ passes through $(1,2)$ . Find $dy/dx$ at that point.

Reveal answer or reference solution

Differentiating with respect to $x$ gives

2x+y+x\,y'+2y\,y'=0

Therefore

y'=-\frac{2x+y}{x+2y},

and at $(1,2)$ , $y'=-4/5$ .

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Implicit tangent slope

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