2.3.28 Gradient and directional derivative

Condition: Given a function \( z=z(x ; y) \), a point \( A\left(x_{0} ; y_{0}\right) \) and a vector \( \vec{a} \). Find: 1) \( \operatorname{grad} z \) at the point \( A: \operatorname{grad} z\left(x_{1}, y_{0}\right) \), 2) derivative at the point \( A \) in the direction of the vector \( \vec{a}: \frac{\partial z}{\partial z}\left(x_{0}, y_{0}\right) \). \[ z=\ln \left(x^{2}+3 y^{2}\right) ; \quad A(1 ; 1) ; \quad \vec{a}=3 \vec{\imath}+2 \vec{\jmath} \]