MathProblemsBank

2.2.90 Derivatives and differentials

Condition: Prove that the function \( f(x, y) \) is differentiable at a given point \( O \) and calculate the differential at this point. \[ f(x, y)=\left\{\begin{array}{c} x^{2}+y^{2} \sin \frac{1}{x^{2}+y^{2}}, x^{2}+y^{2} \neq 0 \\ 0, x^{2}+y^{2}=0 \end{array}, O(0,0)\right. \]

Calculation of derivatives and differentials of first and higher orders of functions of one and many variables, including partial derivatives.

-> Derivatives and differentials