Chapter 13.5, Problem 65ES

(a) Let w be a differentiable function of $x_1,x_2,x_3,\text{and}{x}_4,$ and let each $x_i$ be a differentiable function of t. Find a chain-rule formula for $dw/dt.$

(b) Let w be a differentiable function of $x_1,x_2,x_3,\text{and}{x}_4,$ and let each $xi$ be a differentiable function of ${\upsilon }_1,{\upsilon }_2,\text{and}{\upsilon }_3.$ Find chain-rule formulas for $\partial w/\partial {\upsilon }_1,\partial w/\partial {\upsilon }_2,\text{and}\partial w/\partial {\upsilon }_3.$