5. continuity and differentiation — ગણિત ધોરણ 12 સાયન્સ — Question

==> $x\log x + y\log y + z\log z = \log c$ .....$(i)$

Here $x, y$ are regarded as independent variables and $z $ depends on  $x, y.$

Differentiating $ (i) $ partially  $w.r.t. ‘x’$

$x.\frac{1}{x} + \log x.1 + 0 + \left( {z.\frac{1}{z} + \log z.1} \right)\frac{{\partial z}}{{\partial x}} = 0$

$\therefore $ $\frac{{\partial z}}{{\partial x}} = - \frac{{1 + \log x}}{{1 + \log z}}$.