Let w = f(x, y), where x and y are functions of t. Then according to the chain rule \(\frac{{{\rm{dw}}}}{{{\rm{dt}}}}{\rm{}}\) is equal to
1
\(\frac{{{\rm{dw}}}}{{{\rm{dx}}}}\frac{{{\rm{dx}}}}{{{\rm{dt}}}} + \frac{{{\rm{dw}}}}{{{\rm{dy}}}}\frac{{{\rm{dt}}}}{{{\rm{dt}}}}\)
2
\(\frac{{\partial {\rm{w}}}}{{\partial {\rm{x}}}}\frac{{\partial {\rm{x}}}}{{\partial {\rm{t}}}} + \frac{{\partial {\rm{w}}}}{{\partial {\rm{y}}}}\frac{{\partial {\rm{y}}}}{{\partial {\rm{t}}}}\)
3
\(\frac{{\partial {\rm{w}}}}{{\partial {\rm{x}}}}\frac{{{\rm{dx}}}}{{{\rm{dt}}}} + \frac{{\partial {\rm{w}}}}{{\partial {\rm{y}}}}\frac{{{\rm{dy}}}}{{{\rm{dt}}}}\)
4
\(\frac{{{\rm{dw}}}}{{{\rm{dx}}}}\frac{{\partial {\rm{x}}}}{{\partial {\rm{t}}}} + \frac{{{\rm{dw}}}}{{{\rm{dy}}}}\frac{{\partial {\rm{y}}}}{{\partial {\rm{t}}}}\)