Question Number 2111 by 123456 last updated on 03/Nov/15
$$\mathrm{lets}\:{f}:\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R} \\ $$$$\mathrm{does} \\ $$$$\frac{\partial{f}}{\partial{x}}=\frac{\partial}{\partial{x}}\underset{\mathrm{0}} {\overset{{x}} {\int}}\frac{\partial{f}}{\partial{y}}{dy}\:\:\:? \\ $$
Answered by prakash jain last updated on 03/Nov/15
$${f}={x}^{\mathrm{2}} {y} \\ $$$$\mathrm{LHS}=\mathrm{2}{xy} \\ $$$$\mathrm{RHS}=\mathrm{2}{x} \\ $$$$\mathrm{LHS}\neq\mathrm{RHS} \\ $$$$\mathrm{LHS}\:\mathrm{will}\:\mathrm{be}\:\mathrm{dependent}\:\mathrm{on}\:{y}. \\ $$$$\mathrm{RHS}\:\mathrm{will}\:\:\mathrm{NOT}\:\mathrm{be}\:\mathrm{dependent}\:\mathrm{on}\:{y}. \\ $$