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Multivariable CalculusChallengePartial Derivatives & the Gradient

Partial Derivatives & the Gradient · Challenge problem

Near (u,v)=(1,2)(u,v) = (1,2) the equations x=u+v2x = u + v^2 and y=u2+vy = u^2 + v can be solved for uu and vv as differentiable functions of xx and yy; the point (u,v)=(1,2)(u,v) = (1,2) corresponds to (x,y)=(5,3)(x,y) = (5,3). Find ∂u∂x\dfrac{\partial u}{\partial x} at (x,y)=(5,3)(x,y) = (5,3).