2.2.78 Derivatives and differentials
Condition: Calculate the values of partial derivatives \( f_{x}^{\prime}\left(M_{0}\right), f_{y}^{\prime}\left(M_{0}\right), f_{z}^{\prime}\left(M_{0}\right) \) for a given function \( f(x, y, z) \) at the point \( M_{0}\left(x_{0}, y_{0}, z_{0}\right) \) accurate to two decimal places. \[ f(x, y, z)=27 \sqrt[3]{x+y^{2}+z^{3}}, \quad M_{0}(3,4,2) \]
Calculation of derivatives and differentials of first and higher orders of functions of one and many variables, including partial derivatives.