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Multivariable CalculusHardPartial Derivatives & the Gradient

Partial Derivatives & the Gradient · Hard problem

The curve y=x2y=x^{2} has a point with x>0x>0 at which its tangent LINE is parallel to the gradient of f(x,y)=xyf(x,y)=xy at that same point. Find that xx-coordinate. Give an exact answer in simplest radical form.