$(10\%)$ Compute the first derivative of the following function:

$f(x)=\frac{\sqrt[\phantom{2}]{e^{x^2}-x}}{\sqrt[\phantom{2}]{x}}$

$(15\%)$ Compute the partial derivatives $f_x$ and $f_y$ of the following function:

$f(x_1,x_2)=\frac{x_1^2+2x_2}{-3x_1^2+\sqrt[\phantom{2}]{x_2}}$

$(15\%)$ Solve this constrained optimization problem indicating if the solution$($s$)$ is$($are$)$ a maximum, a minimum, or neither of the two:

$f(x_1,x_2)=5-(x_1-2{)}^2-2(x_2-1{)}^2$ subject $to{x}_1+4x_2=3$