QUESTIONS

For the equation $x^2+y^2-x+y-xy-4=0$ find $y^{\text{'}\text{'}}$ at the point $.$

a$.$ Let $f$ be a function with two variables and

$f(x,y)=e^{-(z^2+y^2)}*sin(x^2+y^2)$

Then find the $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{x}}$ and $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}.(20$p$.)$

b$.$

$f(x)=si{n}^2(cos\sqrt[\phantom{2}]{x})+co{s}^{\text{'}}(e^{\text{'}}),f^{\text{'}}(x)-?$