implicit function

Using implicit differentiation, we have

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Now simply by substituting (x, y, z) = (1,2,1), we get the value -227.712.

Next, we have



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Therefore the tangent line can be given by point slope form
y - y0 = m(x - x0), where m is simply dy/dx.

Last but not least - look out for the case when y = 0, the derivative does not exist - in that case the tangent is a vertical line x = a or x = -a.