t Plane General Formula">
    Consider the function $z=f(x,y)$. Explain why an equation of
    the tangent plane to $f$ at $(x,y)=(a,b)$ is given by
    $$z-f(a,b) = \frac{\partial f}{\partial x}(a,b) (x-a) +
    \frac{\partial f}{\partial y}(a,b) (y-b).$$ Then give an
    equation of the tangent plane to $f(x,y) = x^2+3xy$ at
    $(3,-1)$. [Hint: Use either differential notation or a
    parametrization, or try both ways.]
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  <h1>The Chain Rule</h1>We'll now see how th