In Exercises $1-3,$ begin by drawing a diagram that shows the relations among the variables.
If $w=x^{2}+y-z+$ sin $t$ and $x+y=t,$ find
a. $\left(\frac{\partial w}{\partial y}\right)_{x, z}$ b. $\left(\frac{\partial w}{\partial y}\right)_{z, t}$ c. $\left(\frac{\partial w}{\partial z}\right)_{x, y}$ d. $\left(\frac{\partial w}{\partial z}\right)_{y, t}$ e. $\left(\frac{\partial w}{\partial t}\right)_{x, z}$ f. $\left(\frac{\partial w}{\partial t}\right)_{v, z}$