Chapter 6, Problem 4RE

To determine

Match expression $\frac{\partial }{\partial y}\left(5x^3{y}^7\right)$ in column $A$ with an equivalent expression in column $B$ . Assume that $z=f\left(x,y\right)$ .

  $\boxed{\begin{array}{l}\text{Column A}\text{Column B}\\ \text{1}\text{. }\frac{\partial z}{\partial x}\left(a\right){\displaystyle \underset{2}{\overset{3}{\int }}\frac{1}{2}xdx}\\ \text{2}\text{. }\frac{\partial z}{\partial y}\left(b\right)f_{yx}\\ \text{3}\text{.}\frac{\partial }{\partial x}\left(5x^3{y}^7\right)\left(c\right)f_{xy}\\ \text{4}\text{. }\frac{\partial }{\partial y}\left(5x^3{y}^7\right)\left(d\right){\displaystyle \underset{2}{\overset{3}{\int }}{y}^{3}dy}\\ \text{5}\text{. }\frac{{\partial }^{2}z}{\partial x\partial y}\left(e\right)f_x\\ \text{6}\text{. }\frac{{\partial }^{2}z}{\partial y\partial x}\left(f\right)15x^2{y}^7\\ \text{7}\text{. }{\displaystyle \underset{2}{\overset{3}{\int }}{\displaystyle \underset{0}{\overset{1}{\int }}2x{y}^{3}dxdy}\left(g\right)35x^3{y}^6}\\ \text{8}\text{. }{\displaystyle \underset{2}{\overset{3}{\int }}{\displaystyle \underset{0}{\overset{1}{\int }}2x{y}^{3}dydx}\left(h\right)f_y}\end{array}}$