Find y' if x3 + y3 = 6xy. | Mathematics I 2080

Mathematics I20805 marksNumerical: implicit differentiationReview of derivative

Find y' if $x^3 + y^3 = 6xy$ . [5]

Find y' if $x^3 + y^3 = 6xy$. [5]

Equation (folium of Descartes): $x^3 + y^3 = 6xy$ Find: $y' = \dfrac{dy}{dx}$ Differentiate both sides with respect to $x$ : $\frac{d}{dx}(x^3) + \frac{d}{dx}(y^3) = \frac{d}{dx}(6xy)$ Left side (chain rule on $y^3$ ): $3x^2 + 3y^2\,y'$ Right side (product rule on $6xy$ ): $$6\left(1\cdot y + x...

Equation (folium of Descartes): $x^3 + y^3 = 6xy$ Find: $y' = \dfrac{dy}{dx}$ Differentiate both sides with respect to $x$: $$\frac{d}{dx}(x^3) + \frac{d}{dx}(y^3) = \frac{d}{dx}(6xy)$$ Left side (chain rule on $y^3$): $$3x^2 + 3y^2,y'$$ Right side (product rule on $6xy$): $$6\left(1\cdot y + x...

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