PX275 - A1b - total differentiation

\begin{aligned} d f & = (\frac{\partial f}{\partial x}) d x + (\frac{\partial f}{\partial y}) d y \\ can be written as: \\ \frac{d f}{d x} & = (\frac{\partial f}{\partial x}) + (\frac{\partial f}{\partial y}) \frac{d y}{d x} \end{aligned}

eg: $f (x, y) = x y^{2} + y \sin (x)$ $d f = (y^{2} + y \cos (x)) d x + (2 x y + \sin (x)) d y$