Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

Question Number 2111 by 123456 last updated on 03/Nov/15

lets f:R^2 →R  does  (∂f/∂x)=(∂/∂x)∫_0 ^x (∂f/∂y)dy   ?

$$\mathrm{lets}\:{f}:\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R} \\ $$$$\mathrm{does} \\ $$$$\frac{\partial{f}}{\partial{x}}=\frac{\partial}{\partial{x}}\underset{\mathrm{0}} {\overset{{x}} {\int}}\frac{\partial{f}}{\partial{y}}{dy}\:\:\:? \\ $$

Answered by prakash jain last updated on 03/Nov/15

f=x^2 y  LHS=2xy  RHS=2x  LHS≠RHS  LHS will be dependent on y.  RHS will  NOT be dependent on y.

$${f}={x}^{\mathrm{2}} {y} \\ $$$$\mathrm{LHS}=\mathrm{2}{xy} \\ $$$$\mathrm{RHS}=\mathrm{2}{x} \\ $$$$\mathrm{LHS}\neq\mathrm{RHS} \\ $$$$\mathrm{LHS}\:\mathrm{will}\:\mathrm{be}\:\mathrm{dependent}\:\mathrm{on}\:{y}. \\ $$$$\mathrm{RHS}\:\mathrm{will}\:\:\mathrm{NOT}\:\mathrm{be}\:\mathrm{dependent}\:\mathrm{on}\:{y}. \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com