I. $(5$ pts$)$ Given $f(x,y,z)=xyz+sin(x^2+2y+z^3)$ where $x=t+s$

$y=ln(t+s),z=e^{t+s}$

Find $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{t}}$

II$.(5$ pts$)$ Given $f(x,y)=x^5+y^{\frac{2}{3}}x+\sqrt[\phantom{2}]{x^2-y^2}$

Find $\frac{de{l}^{2}f}{\text{d}\text{e}\text{l}\text{x}\text{d}\text{e}\text{l}\text{y}}$

III. $(5$ pts$)$ Determine particular level curves and graph $z=\sqrt[\phantom{2}]{4-x^2-y^2}$

IV$.(5$ pts$)$ Find and classify critical points of: $f(x,y)=x^3+6xy+3y^2+6x$

V$.$ pts $-10$ pts each