2.3.28 Gradient and Directional Derivative

Condition: Given the function \ (z = z (x; y) \), point \ (a \ left (x_ {0}; y_ {0} \ right) \) and vector \ (\ vec {a} \). Find: 1) \ (\ Operatorname {grad} z \) at the point \ (a: \ OperatorName {grad} z \ left (x_ {1}, y_ {0} \ right) \), 2) derivative \ (a \) towards the vector \ (a \ 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} \]