(Solved): advance math for engineers  1. Find the first order partial derivatives: \( z=\ln \left(y+\sqrt ...

1. Find the first order partial derivatives: \( z=\ln \left(y+\sqrt{x^{2}+y^{2}}\right) \) 2. Find the gradient of the function \( f(x, y)=\ln \left(x^{2}+y^{2}\right) \) at the point \( (3,4) \). 3. Find the derivative of the function \( f(x, y, z)=x y^{3}+y z^{3}+z x^{3} \) at ti \( (-1,2,1) \) in the direction \( \mathbf{A}=3 \mathbf{i}+4 \mathbf{j}-5 \mathbf{k} \).