Section 14.6: Directional Derivatives & Gradient Vector

Show that the equation of the tangent plane to the ellipsoid \(x^2/a^2 + y^2/b^2 + z^2/c^2 = 1\) at the point \((x_0, y_0, z_0)\) can be written as \(\frac{xx_0}{a^2} + \frac{yy_0}{b^2} + \frac{zz_0}{c^2} = 1\)