2.2.68 Derivatives and differentials
Condition: Make sure that the given expression is a total differential \( d U \) and find \( U \). \[ \frac{2 x\left(1-e^{y}\right)}{\left(1+x^{2}\right)^{2}} d x+\frac{e^{y}}{1+x^{2}} d y \]
Calculation of derivatives and differentials of first and higher orders of functions of one and many variables, including partial derivatives.