English: When it is a function of (t,y), I have So this is actually equal to $g^{'}(y) = N(x,y) - \frac{\partial N(t,y)}{\partial t}\ dt\ $, this simply integrate $\frac{\partial M(t,y)}{\partial y}\ dt$, so this goes, simply total derivative of N, $\frac{\partial N(t,y)}{\partial x}\ dt$.
Kannada: ಇದು (t,y) ನ ಕಾರ್ಯವಾಗಿರುವಾಗ, ಇದು ವಾಸ್ತವವಾಗಿ $g^{'}(y) = N(x,y) - \frac{\partial N(t,y)}{\partial t}\ dt\ $ಗೆ ಸಮನಾಗಿರುತ್ತದೆ, ಇದು ಸರಳವಾಗಿ $\frac{\partial M(t,y)}{\partial y}\ dt$ಗೆ ಸಮನಾಗಿರುತ್ತದೆ.