What is the slope of the line tangent to the graph of $x^{2} x y + y^{2} = 7$ $x^2xy+y^2=7$ ?

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Answer 1 · 2015-06-13T16:12:49

Slope= $\frac{- 3 x^{2} y}{2 y + x^{3}}$ $(-3x^2 y)/(2y+x^3)$

Differentiating the equation, it is $x^{3} \frac{d y}{d x} + 3 x^{2} y + 2 y \frac{d y}{d x} = 0$ $x^3 dy/dx +3x^2 y +2y dy/dx=0$

$(x^{3} + 2 y) \frac{d y}{d x} = - 3 x^{2} y$ $(x^3 +2y)dy/dx= -3x^2y$

$\frac{d y}{d x} = \frac{- 3 x^{2} y}{2 y + x^{3}}$ $dy/dx= (-3x^2 y)/ (2y+x^3)$

What is the slope of the line tangent to the graph of x^2xy+y^2=7x2xy+y2=7x^2xy+y^2=7?