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Multivariable CalculusChallengeThe Chain Rule & Implicit Differentiation

The Chain Rule & Implicit Differentiation · Challenge problem

A differentiable function f(x,y)f(x,y) on the half-plane x>0x > 0 satisfies xfx+yfy=3fx f_x + y f_y = 3f everywhere there, and f(1,t)=t2+1f(1, t) = t^2 + 1 for every real tt. Find f(2,4)f(2, 4).