007A Sample Final 1, Problem 8

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A curve is defined implicitly by the equation

x^{3}+y^{3}=6xy.

(a) Using implicit differentiation, compute ${\frac {dy}{dx}}$ .

(b) Find an equation of the tangent line to the curve $x^{3}+y^{3}=6xy$ at the point $(3,3)$ .

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