2.2.66 Derivatives and differentials
condition: Find the first order partial derivatives of the function \( z=z(x, y) \), given implicitly: \[ 3 \tan ^{-1} \frac{z}{y}+2 z^{2} x^{4}+2 z y^{3}=10 \]
Calculation of derivatives and differentials of first and higher orders of functions of one and many variables, including partial derivatives.