2.3.6 Gradient and directional derivative

Problem: Function \( z=z(x, y) \), point \( A\left(x_{0} ; y_{0}\right) \) and vector \( \vec{a} \) are given. It is required to find at point \( A \) : a) the gradient of the function and its value, b) the derivative of \( z \) in the direction of vector \( \vec{a} \). \[ z(x, y)=\ln (5 x+3 y), \quad A(2 ; 2), \quad \vec{a}=\{2 ;-3\} . \]